Limits of weight spaces, Lusztig’s $q$-analogs, and fiberings of adjoint orbits
HTML articles powered by AMS MathViewer
- by Ranee Kathryn Brylinski
- J. Amer. Math. Soc. 2 (1989), 517-533
- DOI: https://doi.org/10.1090/S0894-0347-1989-0984511-X
- PDF | Request permission
References
- Henning Haahr Andersen and Jens Carsten Jantzen, Cohomology of induced representations for algebraic groups, Math. Ann. 269 (1984), no. 4, 487–525. MR 766011, DOI 10.1007/BF01450762
- I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, Structure of representations that are generated by vectors of highest weight, Funkcional. Anal. i Priložen. 5 (1971), no. 1, 1–9 (Russian). MR 0291204, DOI 10.1007/BF01075841
- Walter Borho and Hanspeter Kraft, Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen, Comment. Math. Helv. 54 (1979), no. 1, 61–104 (German, with English summary). MR 522032, DOI 10.1007/BF02566256
- 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, DOI 10.1007/BF01388532
- Phillip A. Griffiths, Hermitian differential geometry, Chern classes, and positive vector bundles, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 185–251. MR 0258070
- R. K. Gupta, Generalized exponents via Hall-Littlewood symmetric functions, Bull. Amer. Math. Soc. (N.S.) 16 (1987), no. 2, 287–291. MR 876966, DOI 10.1090/S0273-0979-1987-15519-4
- R. K. Gupta, Characters and the $q$-analog of weight multiplicity, J. London Math. Soc. (2) 36 (1987), no. 1, 68–76. MR 897675, DOI 10.1112/jlms/s2-36.1.68
- Wim H. Hesselink, Cohomology and the resolution of the nilpotent variety, Math. Ann. 223 (1976), no. 3, 249–252. MR 417195, DOI 10.1007/BF01360956
- Wim H. Hesselink, Characters of the nullcone, Math. Ann. 252 (1980), no. 3, 179–182. MR 593631, DOI 10.1007/BF01420081
- David Kazhdan and George Lusztig, Schubert varieties and Poincaré duality, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203. MR 573434
- 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, DOI 10.1007/BF01389223
- Bertram Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973–1032. MR 114875, DOI 10.2307/2372999
- Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404. MR 158024, DOI 10.2307/2373130
- 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 D. Peterson, A formula for the generalized exponents of representations, manuscript, M.I.T., 1978. J. P. Serre, Espaces fibres algébriques, Séminaire C. Chevalley (Anneaux de Chow et applications), 1958, pp. 1-01-1-37.
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: J. Amer. Math. Soc. 2 (1989), 517-533
- MSC: Primary 17B10; Secondary 14M17, 20G05, 22E47
- DOI: https://doi.org/10.1090/S0894-0347-1989-0984511-X
- MathSciNet review: 984511