×

p-adic analog of the Kazhdan-Lusztig hypothesis. (English) Zbl 0476.22014


MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
20G10 Cohomology theory for linear algebraic groups
20G05 Representation theory for linear algebraic groups
14F30 \(p\)-adic cohomology, crystalline cohomology
14L30 Group actions on varieties or schemes (quotients)
14M12 Determinantal varieties
14M15 Grassmannians, Schubert varieties, flag manifolds
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. V. Zelevinskii, ”Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n),” Ann. Sci. Ecole Norm. Sup., 4e Serie,13, No. 2, 165-210 (1980). · Zbl 0441.22014
[2] A. V. Zelevinskii, ”Classification of irreducible noncuspidal representations of the group GLn over a p -adic field,” Funkts. Anal. Prilozhen.,11, No. 1, 67-68 (1977). · Zbl 0363.22012
[3] A. V. Zelevinskii, ”The ring of representations of the group GL(n) over a p -adic field,” Funkts. Anal. Prilozhen.,11, No. 3, 78-79 (1977). · Zbl 0368.14006
[4] D. Kazhdan and G. Lusztig, ”Representations of Coxeter groups and Hecke algebras,” Invent. Math.,53, No. 2, 165-184 (1979). · Zbl 0499.20035
[5] D. Kazhdan and G. Lusztig, Schubert Varieties and Poincare Duality, Preprint.
[6] J. C. Dixmier, Enveloping Algebras, Elsevier (1977).
[7] I. N. Bernshtein, I. M. Gel’fand, and S. I. Gel’fand, ”On a certain category ofg-modules,” Funkts. Anal. Prilozhen.,10, No. 2, 1-8 (1976). · Zbl 0375.35048
[8] M. Goreskii and R. MacPherson, ”Intersection homology theory,” Topology,19, No. 2, 135-162 (1980). · Zbl 0448.55004
[9] R. Steinberg, Lectures on Chevalley Groups, Yale Univ. Press, New Haven (1968). · Zbl 1196.22001
[10] R. A. Liebler and M. R. Vitale, ”Ordering the partition characters of the symmetric group,” J. Algebra,25, No. 3, 487-489 (1973). · Zbl 0274.20016
[11] C. W. Curtis, ”Truncation and duality in the character ring of a finite group of Lie type,” J. Algebra,62, 320-332 (1980). · Zbl 0426.20006
[12] D. Alvis, ”The duality operation in the character ring of a finite Chevalley group,” Bull. Am. Math. Soc., New Series,1, 907-911 (1979). · Zbl 0485.20029
[13] V. S. Pyasetskii, ”Linear Lie groups that act with a finite number of orbits,” Funkts. Anal. Prilozhen.,9, No. 4, 85-86 (1975). · Zbl 0319.32007
[14] P. Deligne, Cohomologie Etale, Lect. Notes Math., Vol. 569, Springer-Verlag, Berlin-New York (1977).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.