Generalized Robinson-Schensted Algorithms for Real Groups

International Mathematics Research Notices

Volumn 1999, Issue 15, 1999, Pages

  Trapa, Peter E ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012944253     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. [BV] D. Barbasch and D. A. Vogan Jr., "Weyl group representations and nilpotent orbits" in Representation Theory of Reductive Groups (Park City, UT, 1982), P. Trombi ed., Progr. Math. 40, Birkhäuser, Boston, 1983, 21-33.
2. [BoBr] W. Borho and J.-L. Brylinski, Differential operators on homogeneous spaces, III, Invent. Math. 80 (1985), 1-68.
3. [CMc] D. H. Collingwood and W. M. McGovern, Nilpotent Orbits in Semisimple Lie Algebras, Van Nostrund Reinhold Math. Ser., Van Nostrund Reinhold Co., New York, 1993.
4. [D] J. M. Douglass, An involution of the variety of flags fixed by a unipotent linear transformation, Adv. in Appl. Math. 17 (1996), 357-379.
5. n-1 groups, Amer. J. Math. 115 (1993), 305-369.
6. [GrV] W. Graham and D. A. Vogan Jr., "Geometric quantization for nilpotent coadjoint orbits" in Geometry and Representation Theory of Real and p-adic Groups (Córdoba, 1995), Progr. Math. 138, Birkhäuser, Boston, 1998, 69-137.
7. [H] R. Hotta, On Joseph's construction of Weyl group representations, Tôhoku Math. J. (2) 36 (1984), 49-74.
8. [J] J. C. Jantzen, Einhüttende Algebren helbeinfacher Lie-Algebren, Ergeb. Math. Grenzegeb. (3) 3, Springer, Berlin, 1983.
9. [Jo] A. Joseph, On the variety of a highest weight module, J. Algebra 88 (1984), 238-278.
10. [KT] M. Kashiwara and T. Tanisaki, The characteristic cycles of holonomic systems on a flag manifold related to the Weyl group algebra, Invent. Math. 77 (1984), 185-198.
11. [KaL] D. Kazhdan and G. Lusztig, A topological approach to Springer's representations, Adv. in Math. 38 (1980), 222-228.
12. [KoR] B. Kostant and S. Rallis, Orbits and representatives associated with symmetric spaces, Amer. J. Math. 93 (1971), 753-809.
13. [Mc1] W. M. McGovern, Cells of Harish-Chandra modules for real classical Lie groups, Amer. J. Math. 120 (1998), 211-228.
14. [Mc2] _, On the Spaltenstein-Steinberg map for complex classical groups, preprint, 1998.
15. [Ma] T. Matsuki, The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan 31 (1979), 331-357.
16. [MaO] T. Matsuki and T. Oshima, "Embeddings of discrete series into principal series" in The Orbit Method in Representation Theory, Progr. Math. 82, Birkhäuser, Boston, 1988, 147-175.
17. [RSp] R. W. Richardson and T. A. Springer, The Bruhat order on symmetric varieties, Geom. Dedicata 35 (1990), 389-436.
18. [Ro] W. Rossmann, Invariant eigendistributions on a semisimple Lie algebra and homology classes on the conormal variety, II: Representations of Weyl groups, J. Funct. Anal. 96 (1991), 155-193.
19. [Sa] B. E. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, Wadsworth & Brooks/Cole Math. Ser., Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991.
20. [ScV] W. Schmid and K. Vilonen, Characteristic cycles of constructible sheaves, Invent. Math. 124 (1994), 451-502.
21. [Sp1] N. Spaltenstein, On the fixed point set of a unipotent element on the variety of Borel subgroups, Topology 16 (1977), 203-204.
22. [Sp2] _, Classes unitpotentes et sous-groupes Borel, Lecture Notes in Math. 946, Springer, Berlin, 1982.
23. [Spr1] T. A. Springer, "Geometric questions arising in the study of unipotent elements" in The Santa Cruz Conference on Finite Groups (Santa Cruz, CA, 1979), Proc. Sympos. Pure Math. 37, Amer. Math. Soc., Providence, 1980, 255-264.
24. [Spr2] _, "Schubert varieties and generalizations" in Representation Theories and Algebraic Geometry (Montreal, PQ, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514, Kluwer Acad. Publ., Dordrecht, 1998, 413-440.
25. [St1] R. Steinberg, On the desingularization of the unipotent variety, Invent. Math. 36 (1976), 209-224.
26. [St2] _, An occurrence of the Robinson-Schensted algorithm, J. Algebra 113 (1988), 523-528.
27. [T] T. Tanisaki, "Characteristic varieties of highest weight modules and primitive quotients" in Representations of Lie groups, Kyoto, Hiroshima, 1986, Adv. Stud. Pure Math. 14, Academic Press, Boston, 1988, 1-30.
28. [Te] I. Terada, Brauer diagrams, updown tableaux, and nilpotent matrices, preprint, 1999.
29. q(λ) modules for U(p, q), preprint, 1998.
30. [vL] M. van Leeuwen, A Robinson-Schensted algorithm in the geometry of flags for classical groups, Rijksuniversiteit Thesis, Utrecht, 1989.
31. [V1] D. A. Vogan Jr., Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math. 48 (1978), 75-98.
32. [V2] _, Irreducible characters of semisimple Lie groups, IV: Character multiplicity duality, Duke Math. J. 49 (1982), 943-1073.
33. [V3] _, Irreducible characters of semisimple Lie groups, III: Proof of Kazhdan-Lusztig conjecture in the integral case, Invent. Math. 71 (1983), 381-417.
34. [V4] _, "Associated varieties and unipotent representations" in Harmonic Analysis on Reductive Groups (Brunswick, ME, 1989), Progr. Math. 101, Birkhäuser, Boston, 1991, 315-388.
35. [VZ] D. A. Vogan Jr. and Gregg Zuckerman, Unitary representations with nonzero cohomology, Compositio Math. 53 (1984), 51-90.
36. [Y] A. Yamamoto, Orbits in the flag variety and images of the moment map for classical groups, I, Represent. Theory 1 (1997), 329-404.
37. [Z] R. Zierau, Representation in Dolbeault Cohomology, to appear in the IAS/Park City Mathematics Ser.