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Generalized exponents via Hall-Littlewood symmetric functions
Author:
R. K. Gupta
Journal:
Bull. Amer. Math. Soc. 16 (1987), 287-291
MSC (1985):
Primary 22E46, 17B10, 05A15; Secondary 05A17
MathSciNet review:
876966
Full-text PDF
References |
Similar Articles |
Additional Information
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E.
M. Friedlander and B.
J. Parshall, On the cohomology of algebraic and related finite
groups, Invent. Math. 74 (1983), no. 1,
85–117. MR
722727 (85d:20035), http://dx.doi.org/10.1007/BF01388532
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R.
K. Gupta, Characters and the 𝑞-analog of weight
multiplicity, J. London Math. Soc. (2) 36 (1987),
no. 1, 68–76. MR 897675
(88i:17010), http://dx.doi.org/10.1112/jlms/s2-36.1.68
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[G2] R. K. Gupta, Stability of polynomial powers of gl (in preparation).
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P.
Hanlon, On the decomposition of the tensor algebra of the classical
Lie algebras, Adv. in Math. 56 (1985), no. 3,
238–282. MR
792707 (88a:17011), http://dx.doi.org/10.1016/0001-8708(85)90035-0
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H. Hesselink, Characters of the nullcone, Math. Ann.
252 (1980), no. 3, 179–182. MR 593631
(82c:17004), http://dx.doi.org/10.1007/BF01420081
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Shin-ichi
Kato, Spherical functions and a 𝑞-analogue of
Kostant’s weight multiplicity formula, Invent. Math.
66 (1982), no. 3, 461–468. MR 662602
(84b:22030), http://dx.doi.org/10.1007/BF01389223
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Kostant, Lie group representations on polynomial rings, Amer.
J. Math. 85 (1963), 327–404. MR 0158024
(28 #1252)
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George
Lusztig, Singularities, character formulas, and a 𝑞-analog
of weight multiplicities, Analysis and topology on singular spaces,
II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math.
France, Paris, 1983, pp. 208–229. MR 737932
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G. Macdonald, Symmetric functions and Hall polynomials, The
Clarendon Press Oxford University Press, New York, 1979. Oxford
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(84g:05003)
-
Richard
P. Stanley, The stable behavior of some characters of
𝑆𝐿(𝑛,𝐶), Linear and Multilinear
Algebra 16 (1984), no. 1-4, 3–27. MR 768993
(86e:22025), http://dx.doi.org/10.1080/03081088408817606
- [FP] E. M. Friedlander and B. J. Parshall, On the cohomology of algebraic and related finite groups. Invent. Math. 74 (1983), 85-117. MR 722727
- [Gl] R. K. Gupta, Characters and the q-analog of weight multiplicity, I.H.E.S. preprint M/86/6 (submitted for publication). MR 897675
- [G2] R. K. Gupta, Stability of polynomial powers of gl (in preparation).
- [Hn] P. Hanlon, On the decomposition of the tensor algebra of the classical Lie algebras, Adv. in Math. 56 (1985), 238-282. MR 792707
- [Hs] W. H. Hesselink, Characters of the nullcone, Math. Ann. 252 (1980), 179-182. MR 593631
- [Ka] S. Kato, Spherical functions and a q-analogue of Kostant's weight multiplicity formula, Invent. Math. 66 (1982), 461-468. MR 662602
- [K] B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327-404. MR 158024
- [L] G. Lusztig, Singularities, character formulas, and a q-analog of weight multiplicities, Analyse et Topologie sur les Espaces Singuliers (II-III), Astérisque 101-102 (1983), 208-227. MR 737932
- [M] I. G. Macdonald, Symmetrie functions and Hall polynomials, Clarendon Press, Oxford, 1979. MR 553598
- [S] R. Stanley, The stable behavior of some characters of SL(n, C), Linear and Multilinear Algebra 16 (1984), 3-27. MR 768993
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1987-15519-4
PII:
S 0273-0979(1987)15519-4
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