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Publications since 1993

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 $\frak g$-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, $\frak g$-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 sl(2)-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 sl(2)-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).