Selected Publications of Dmitri Panyushev

  1. Complexity and rank of double cones and tensor product decompositions, Comment. Math. Helvetici 68 (1993), 455-468.
  2. The Jacobian modules of a Lie algebra and geometry of commuting varieties, Compositio Math. 94 (1994), 181-199.
  3. Complexity and nilpotent orbits, Manuscripta Math. 83 (1994), 223-237.
  4. (with D. Gurevich) On Poisson pairs associated to modified R-matrices, Duke Math. J. 73 (1994), 249-255.
  5. Multiplicities of weights of some representations and convex polytopes, Funct. Anal. Appl. 28 (1994), 293-295.
  6. A restriction theorem and the Poincare series for U-invariants, Math. Annalen 301 (1995), 655-675.
  7. On homogeneous spaces of rank one, Indag. Math. 6 (1995), 315-323.
  8. Good properties of algebras of invariants and defect of linear representations, Journal of Lie Theory 5 (1995), 81-99.
  9. Reductive group actions on affine varieties and their doubling, Annales l'Institut Fourier 45 (1995), 929-950.
  10. On double cones and tensor product decompositions, Uspekhi matem. Nauk 51 no. 2 (1996), 171-172 (Russian).
  11. Cones of highest weight vectors, weight polytopes, and Lusztig's $q$-analog, Transformation Groups 2 (1997), 91-115.
  12. On deformation Method in Invariant Theory, Ann. l'Institut Fourier 47 (1997), 985-1012.
  13. On the conormal bundle of a G-stable subvariety, Manuscripta Math. 99 (1999), 185-202.
  14. On actions of a maximal torus on orbits of highest weight vectors, J. Algebra 212 (1999), 683-702.
  15. Actions of "nilpotent tori" on $G$-varieties, Indagationes Math. 10(4) (1999), 565-579.
  16. Parabolic subgroups with Abelian unipotent radical as a testing site for Invariant Theory, Can. J. Math. 51(3) (1999), 616-635.
  17. (with E.B. Vinberg) An infinitesimal characterization of the complexity of homogeneous spaces, Transformation Groups 4 (1999), 97-101.
  18. On spherical nilpotent orbits and beyond, Ann. Inst. Fourier 49 (1999), 1453-1476.
  19. Complexity and rank of actions in invariant theory, J. Math. Sci (New York) 95 (1999), 1925-1985.
  20. Nilpotent pairs in semisimple Lie algebras and their characteristics, Intern. Math. Res. Notices, no. 1 (2000), 1-21.
  21. Nilpotent pairs, dual pairs, and sheets, J. Algebra 240 (2001), 635-664.
  22. (with A.G. Elashvili) A classification of the principal nilpotent pairs in simple Lie algebras and related problems, J. London Math. Soc. 63 (2001), 299-318.
  23. The exterior algebra and `Spin' of an orthogonal 𝔤-module, Transformation Groups 6 (2001), 371-396 gzipped PS.
  24. Isotropy representations, eigenvalues of a Casimir element, and commutative Lie subalgebras, J. London Math. Soc. 64 (2001), 61-80. gzipped PS.
  25. (with G. Röhrle) Spherical orbits and abelian ideals, Adv. in Math. 159 (2001), 229-246. PDF(Jour.).
  26. Inductive formulas for the index of seaweed Lie algebras, Moscow Math. J. 1 (2001), 221-241. gzipped PS.
  27. (with D.N. Akhiezer) Multiplicities in the branching rules and the complexity of homogeneous spaces, Moscow Math. J. 2 (2002), 17-33. gzipped PS.
  28. On covariants of reductive algebraic groups, Indagationes Math. 13 (2002), 125-129. PDF(Jour.)
  29. The index of a Lie algebra, the centraliser of a nilpotent element, and the normaliser of the centraliser, Math. Proc. Camb. Phil. Soc. 134 (2003), 41-59. gzipped PS.
  30. Abelian ideals of a Borel subalgebra and long positive roots, Intern. Math. Res. Notices, no. 35 (2003), 1889-1913. PDF(Jour.)
  31. Some amazing properties of spherical nilpotent orbits, Math. Zeitschrift, 245 (2003), 557-580. PDF
  32. On the irreducibility of commuting varieties associated with involutions of simple Lie algebras, Funkt. Analiz i ego prilozh. 38 , no.1 (2004), 47-55 (in Russian). gzipped PS.
  33. AD-nilpotent ideals of a Borel subalgebra: generators and duality, J. Algebra 274 (2004), 822-846 (math.RT/0303107).
  34. Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces, Europ. J. Combinatorics 25 (2004), 93-112. PDF(Jour.)
  35. Regions in the dominant chamber and nilpotent orbits, Bull. Sci. Math. 128 (2004), 1-6. PDF(Jour.)
  36. Weight multiplicity free representations, 𝔤-endomorphism algebras, and Dynkin polynomials, J. London Math. Soc. 69, Part 2 (2004), 273-290. PDF(Jour.)
  37. Long Abelian ideals, Adv. Math. 186 (2004), 307-316.
  38. On reachable elements and the boundary of nilpotent orbits in simple Lie algebras, Bull. Sci. Math. 128 (2004), 859-870.
  39. On Invariant Theory of θ-groups, J. Algebra 283 (2005), 655-670.
  40. (with G.Röhrle) On spherical ideals of Borel subalgebras, Archiv der Math. 84 (2005), 225-232. [PDF]
  41. An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras, Ann. Inst. Fourier 55 (2005), no. 3, 693-715.
  42. Ideals of Heisenberg type and minimax elements of affine Weyl groups, in: Amer. Math. Soc. Transl., Series 2. "Lie Groups and Invariant Theory" (E.B.Vinberg, Ed.) 213 (2005), 191-213 (math.RT/0311347).
  43. Normalizers of ad-nilpotent ideals, Europ. J. Combinatorics 27 (2006), 153-178.
  44. The poset of positive roots and its relatives, J. Alg. Combinatorics 23 (2006), 79-101 (math.CO/0502385).
  45. (with O.Yakimova) The index of representations associated with stabilisers, J. Algebra, 302 (2006), 280-304.
  46. Commutative subalgebras and sphericity in Z2-graded Lie algebras, Bull. London Math. Soc., 38, Part 5 (2006), 753-763.
  47. Semi-direct products of Lie algebras, their invariants and representations, Publ. R.I.M.S., 43, no.4 (2007), 1199-1257 (math.AG/0506579).
  48. On the coadjoint representation of Z2-contractions of reductive Lie algebras, Adv. Math., 213 (2007), 380-404 (math.RT/0610493).
  49. (with A.Premet and O.Yakimova) On symmetric invariants of centralisers in reductive Lie algebras, J. Algebra, 313 (2007), 343-391 (math.RT/0610049).
  50. (with O.Yakimova) Symmetric pairs and associated commuting varieties, Math. Proc. Cambr. Phil. Soc. 143 (2007), 307-321 (math.AG/0601534).
  51. Two results on centralisers of nilpotent elements, J. Pure Applied Algebra 212 (2008), 774-779.
  52. (with O.Yakimova) The argument shift method and maximal commutative subalgebras of Poisson algebras, Math. Res. Letters, 15 (2008), 239-249.
  53. (with O.Yakimova) The PRV-formula for tensor product decompositions and its applications, Funct. Anal. Appl., 42, no.1 (2008), 45-52.
  54. Adjoint vector fields and differential operators on representation spaces, Bull. London Math. Soc., 40, no.6 (2008), 1045-1064 (arXiv: 0808.2120).
  55. On orbits of antichains of positive roots, Europ. J. Combinatorics, 30, no.2 (2009), 586-594.
  56. Periodic automorphisms of Takiff algebras, contractions, and θ-groups, Transformation Groups, 14, no.2 (2009), 463-482 (arXiv: 0710.2113).
  57. On the Dynkin index of a principal 𝔰𝔩2-subalgebra, Adv. Math., 221, no.4 (2009), 1115-1121 (arXiv: 0903.0398).
  58. Properties of weight posets for weight multiplicity free representations, Moscow Math. J., 9, no. 4 (2009), 867--883 (arXiv: 0810.2919).
  59. Actions of the derived group of a maximal unipotent subgroup on G-varieties, IMRN, 2010 (2010), no. 4, 674-700 (arXiv: 0812.1343).
  60. Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles, Selecta Math., 16 (2010), 315-342 (arXiv: 0904.3721).
  61. On divisible weighted Dynkin diagrams and reachable elements, Transformation Groups, 15 (2010), 983-999 arXiv: 1002.4854.
  62. (with E.B. Vinberg) The work of Vladimir Morozov on Lie algebras, Transformation Groups, 15 (2010), 1001-1013.
  63. Fredman's reciprocity, invariants of abelian groups, and the permanent of the Cayley table, J. Algebraic Combin., 33 (2011), 111-125 PDF (Journ.).
  64. Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram, J. Algebra, 344 (2011), 197-204 (arXiv: 1008.1850).
  65. Invariants of a maximal unipotent subgroup and equidimensionality, Bull. Sci. Math., 136 (2012), 149-161 (Preprint series of CRC 701 University of Bielefeld, Preprint 11110).
  66. Invariant theory of little adjoint modules, J. Lie Theory, 22 (2012), 803-816 (arXiv: 1205.5200).
  67. Quotients by actions of the derived group of a maximal unipotent subgroup, Pacific J. Math., 256 (2012), 381-405 (arXiv: 1009.4051).
  68. Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals, J. Combinatorics, 3 (2012), 63-89 (math.CO/0502386).
  69. (with O.Yakimova) On a remarkable contraction of semisimple Lie algebras, Ann. Inst. Fourier, 62, no.6 (2012), 2053-2068 (arXiv: 1107.0702).
  70. Commuting involutions and degenerations of isotropy representations, Transformation Groups, 18, no.2 (2013), 507-537 (arXiv: 1104.5472).
  71. Commuting involutions of Lie algebras, commuting varieties, and simple Jordan algebras, Algebra & Number Theory, 7, no.6 (2013), 1505-1534 (arXiv: 1210.3785).
  72. (with O.Yakimova) Parabolic contractions of semisimple Lie algebras and their invariants, Selecta Math., 19 (2013), 699-717 (arXiv: [math.AG] 1301.0249).
  73. Wide subalgebras of semisimple Lie algebras, Algebras and Repr. Theory, 17, no.3 (2014), 931-944 (arXiv: [math.RT] 1301.0488).
  74. Abeian ideals of a Borel subalgebra and root systems, J. Europ. Math. Soc., 16 (2014), 2693-2708 (arXiv: 1205.5983).
  75. (with O.Yakimova) On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras, Bull. Sci. Math., 138 (2014), 705-720 (arXiv: 1312.1872).
  76. The Dynkin index and 𝔰𝔩2-subalgebras of simple Lie algebras, J. Algebra, 430 (2015), 15-25 (arXiv: 1311.3170).
  77. Antichains in weight posets associated with gradings of simple Lie algebras, Math. Z., 281 (2015), 1191-1214 (arXiv: 1411.7683).
  78. Minimal inversion complete sets and maximal abelian ideals, J. Algebra, 445 (2016), 163-180 (arXiv: 1505.00653).
  79. Normalisers of abelian ideals of Borel subalgebras and ℤ-gradings of a simple Lie algebra, J. Lie Theory, 26 (2016), 659-672 (arXiv: 1512.08092).
  80. Weight posets associated with gradings of simple Lie algebras, Weyl groups, and arrangements of hyperplanes, J. Algebraic Combin., 44, no. 2 (2016), 325-344 (arXiv: 1412.0987).
  81. On Lusztig's q-analogues of all weight multiplicities of a representation, In: W. Ballmann, C. Blohmann, G. Faltings, P. Teichner, D. Zagier (Eds.): "Arbeitstagung Bonn 2013. In Memory of Friedrich Hirzebruch", Progr. Math. 319, Birkhäuser 2016, 289-305 (arXiv: 1406.1453).
  82. (with O.Yakimova) On seaweed subalgebras and meander graphs in type C, Pacific J. Math., 285, no. 2 (2016), 485-499, (arXiv: 1601.00305).
  83. On the orbits of a Borel subgroup in abelian ideals, Transformation Groups, 22, no. 2 (2017), 503-524 (arXiv: 1407.6857).
  84. (with O.Yakimova) Semi-direct products of Lie algebras and covariants, J. Algebra, 290 (2017), 283-315 (arXiv: 1705.02631).
  85. (with O.Yakimova) Symmetric invariants related to representations of exceptional simple groups, Труды Моск. Матем. Об-ва, т. 78 (2017), вып. 2, с. 195-207 (= Trans. Mosc. Math. Soc., 78 (2017), 161-170).
  86. Abelian ideals and amazing roots, Intern. J. Math., 28, no. 14 (2017), article 1750105 (9 pages) (DOI).
  87. (with O.Yakimova) On seaweed subalgebras and meander graphs in type D, J. Pure Applied Algebra, 222, no. 11 (2018), 3414-3431 (1702.07879).
  88. (with O.Yakimova) Nilpotent subspaces and nilpotent orbits, J. Austral. Math. Soc., 106 (2019), 104-126 DOI, 1601.03264.
  89. (with O.Yakimova) Semi-direct products involving Sp2n or Spinn with free algebras of symmetric invariants, In: M. Gorelik, V. Hinich, A. Melnikov (Eds.): "Representations and Nilpotent Orbits of Lie Algebraic Systems: In Honour of the 75th Birthday of Tony Joseph", Progr. Math. 330, Basel Birkhäuser, (2019) 441-470. DOI, 1802.07131.
  90. (with O.Yakimova) Takiff algebras with polynomial rings of symmetric invariants, Transformation Groups, 25 (2020), 609-624 DOI, 1710.03180.
  91. Abelian ideals of a Borel subalgebra and root systems, II, Algebras and Representation Theory, 23 (2020), 1487-1498 DOI, 1805.02057.
  92. Glorious pairs of roots and abelian ideals of a Borel subalgebra, J. Algebraic Combin., 52 (2020), 505-525. DOI, 1809.10115.
  93. (with O.Yakimova) Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties, Math. Z., 295 (2020), 101-127. DOI, 1902.09221.
  94. Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications, Adv. Math., 374 (2020), article 107390, DOI, 1912.00341.
  95. (with O.Yakimova) Compatible Poisson brackets associated with 2-splittings and Poisson commutative subalgebras of 𝒮(𝔤), J. London Math. Soc., 103 (2021), 1577-1595, DOI, 2009.05271.