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2016 | OriginalPaper | Chapter

On Lusztig’s q-Analogues of All Weight Multiplicities of a Representation

Author : Dmitri I. Panyushev

Published in: Arbeitstagung Bonn 2013

Publisher: Springer International Publishing

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Abstract

The ground field \(\mathbb{k}\) is algebraically closed and of characteristic zero. Let G be a connected semisimple algebraic group, and T a maximal torus inside a Borel subgroup B.

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Literature
[AC89]
[AC12]
go back to reference E. Akyildiz, J.B. Carrell, Betti numbers of smooth Schubert varieties and the remarkable formula of Kostant, Macdonald, Shapiro, and Steinberg. Mich. Math. J. 61, 543–553 (2012)MathSciNetCrossRefMATH E. Akyildiz, J.B. Carrell, Betti numbers of smooth Schubert varieties and the remarkable formula of Kostant, Macdonald, Shapiro, and Steinberg. Mich. Math. J. 61, 543–553 (2012)MathSciNetCrossRefMATH
[br94]
go back to reference A. Broer, Normality of some nilpotent varieties and cohomology of line bundles on the cotangent bundle of the flag variety, in Lie Theory and Geometry, ed. by J.-L. Brylinski et al. Progress in Mathematics, vol. 123 (Boston, Birkhäuser, 1994), pp. 1–19 A. Broer, Normality of some nilpotent varieties and cohomology of line bundles on the cotangent bundle of the flag variety, in Lie Theory and Geometry, ed. by J.-L. Brylinski et al. Progress in Mathematics, vol. 123 (Boston, Birkhäuser, 1994), pp. 1–19
[Br97]
go back to reference A. Broer, A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles. J. Reine Angew. Math. 493, 153–169 (1997)MathSciNetMATH A. Broer, A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles. J. Reine Angew. Math. 493, 153–169 (1997)MathSciNetMATH
[B89]
go back to reference R.K. Brylinski, Limits of weight spaces, Lusztig’s q-analogs, and fiberings of adjoint orbits. J. Am. Math. Soc. 2, 517–533 (1989)MathSciNetMATH R.K. Brylinski, Limits of weight spaces, Lusztig’s q-analogs, and fiberings of adjoint orbits. J. Am. Math. Soc. 2, 517–533 (1989)MathSciNetMATH
[gr92]
[G87-2]
[Ka82]
[Ko59]
go back to reference B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Am. J. Math. 81, 973–1032 (1959)MathSciNetCrossRefMATH B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Am. J. Math. 81, 973–1032 (1959)MathSciNetCrossRefMATH
[Lu83]
go back to reference G. Lusztig, Singularities, character formulas, and a q-analog of weight multiplicities. Analyse et Topologie Sur Les Espaces Singuliers (II–III). Astérisque, vol. 101–102 (Société Mathématique de France, Paris, 1983), pp. 208–227 G. Lusztig, Singularities, character formulas, and a q-analog of weight multiplicities. Analyse et Topologie Sur Les Espaces Singuliers (II–III). Astérisque, vol. 101–102 (Société Mathématique de France, Paris, 1983), pp. 208–227
[P04]
go back to reference D. Panyushev, Weight multiplicity free representations, \(\mathfrak{g}\) -endomorphism algebras, and Dynkin polynomials. J. Lond. Math. Soc. 69, Part 2, 273–290 (2004) D. Panyushev, Weight multiplicity free representations, \(\mathfrak{g}\) -endomorphism algebras, and Dynkin polynomials. J. Lond. Math. Soc. 69, Part 2, 273–290 (2004)
[P10]
go back to reference D. Panyushev, Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles. Sel. Math. (New Series) 16, 315–342 (2010)MathSciNetCrossRefMATH D. Panyushev, Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles. Sel. Math. (New Series) 16, 315–342 (2010)MathSciNetCrossRefMATH
[S90]
go back to reference H. Samelson, Notes on Lie Algebras. Universitext, 2nd edn. (Springer, New York, 1990), xii+162 pp. H. Samelson, Notes on Lie Algebras. Universitext, 2nd edn. (Springer, New York, 1990), xii+162 pp.
[V06]
go back to reference S. Viswanath, A note on exponents vs root heights for complex simple Lie algebras. Electr. J. Comb. 13, # N22, 5 pp. (2006) S. Viswanath, A note on exponents vs root heights for complex simple Lie algebras. Electr. J. Comb. 13, # N22, 5 pp. (2006)
Metadata
Title
On Lusztig’s q-Analogues of All Weight Multiplicities of a Representation
Author
Dmitri I. Panyushev
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-43648-7_10

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