Brauer Diagrams, Updown Tableaux and Nilpotent Matrices

Journal of Algebraic Combinatorics

Volumn 14, Issue 3, 2001, Pages 229-267

  Terada, Itaru ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Brauer algebra; Nilpotent matrix; Robinson Schensted correspondence; Symplectic form; Young diagram

Indexed keywords

EID: 0035507250     PISSN: 09259899     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012776203570     Document Type: Article

References (41)

1. G. Benkart and A. Ram, A letter dated October 28 (1990).
2. A. Berele, "A Schensted-type correspondence for the symplectic group," J. Conibin. Theory Ser. A 43 (1986), 320-328.
3. A. Borel, Linear Algebraic Groups, 2nd Edition, Graduate Texts in Mathematics, Vol. 126, Springer-Verlag, New York, 1991.
4. R. Brauer, "On algebras which are connected with the semisimple continuous groups," Ann. of Math. 38 (1937), 857-872.
5. e Session, Alghero, 1988, pp. 57-78, Publ. Inst. Rech. Math. Av. 372/S-20, IRMA Strasbourg/Univ. Louis Pasteur, Strasbourg, 1988.
6. P. Edelman and C. Greene, "Balanced tableaux," Advances in Math. 63 (1987), 42-99.
7. L. Favreau, "Combinatoire des tableaux oscillants et des polynômes de Bessel," Ph.D. Thesis, LaBRI/Univ. Bordeaux I, 1991, Publications du LACIM, Vol. 7, LACIM/Univ. du Québec à Montréal, Montréal, 1991.
8. S.V. Fomin, "Generalized Robinson-Schensted-Knuth correspondence," Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 155 (1986), 156-175, 195 (Russian); English transl., J. Soviet Math. 41 (1988), 979-991.
9. S.V. Fomin, "Generalized Robinson-Schensted-Knuth correspondence," Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 155 (1986), 156-175, 195 (Russian); English transl., J. Soviet Math. 41 (1988), 979-991.
10. E.R. Gansner, "Acyclic digraphs, Young tableaux and nilpotent matrices," SIAM J. Algebraic Discrete Methods 2 (1981), 429-440.
11. I.M. Gessel, "Counting paths in Young's lattice," J. Statist. Plann. Inference 34 (1993), 125-134.
12. C. Greene, "An extension of Schensted's theorem," Advances in Math. 14 (1974), 254-265.
13. J.E. Humphreys, Introduction to Linear Algebraic Groups, Graduate Texts in Mathematics, Vol. 21, Springer-Verlag, New York, 1975.
14. W. Kraskiewicz, "Reduced decompositions in hyperoctahedral groups," C.R. Acad. Sci. Paris, Ser. I Math. 309 (1989), 903-907.
15. C. Krattenthaler, "Oscillating tableaux and nonintersecting lattice paths," J. Statist. Plann. Inference 54 (1996), 75-85.
16. T.-K. Lam, "A variation of Kraśkiewicz insertion and shifted tableaux," in The 8th International Conference on Formal Power Series and Algebraic Combinatorics: Extended Abstracts, Minneapolis, 1996, Univ. of Minnesota, 1996, pp. 307-316.
17. T. Matsuki, "The orbits of affine symmetric spaces under the action of minimal parabolic subgroups," J. Math. Soc. Japan 31 (1979), 331-357.
18. T. Matsuki and T. Oshima, "Embeddings of discrete series into principal series," in The Orbit Method in Representation Theory, Progress in Mathematics, Vol. 82, Copenhagen, 1988, Birkhäuser, Boston, 1990, pp. 147-175.
19. n-modules, and Robinson-Schensted-Knuth correspondence," in The 8th International Conference on Formal Power Series and Algebraic Combinatorics: Extended Abstracts, Minneapolis, 1996, Univ. of Minnesota, 1996, pp. 391-402.
20. R.A. Proctor, "Reflection and algorithm proofs of some more Lie group dual pair identities," J. Combin. Theory Ser. A 62 (1993), 107-127.
21. R.W. Richardson and T. A. Springer, "Combinatorics and geometry of K -orbits on the flag manifold," in Linear Algebraic Groups and Their Representations, Contemporary Math. Vol. 153, Los Angeles, 1992, Amer. Math. Soc., Providence, 1993, pp. 109-142.
22. G. de B. Robinson, "On the representations of the symmetric group," Amer. J. Math. 60 (1938), 746-760.
23. T.W. Roby, "Applications and extensions of Fomin's generalization of the Robinson-Schensted correspondence to differential posets," Ph.D. Thesis, M.I.T., 1991.
24. W. Rossmann, "The structure of semisimple symmetric spaces," Canad. J. Math. 131 (1979), 157-180.
25. B.E. Sagan, "Shifted tableaux, Schur Q-functions, and a conjecture of R. Stanley," J. Combin. Theory Ser. A 45 (1987), 62-103.
26. B.E. Sagan, The Symmetric Group, Wadsworth & Brooks/Cole, Pacific Grove, 1991; 2nd Edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York, 2001.
27. B.E. Sagan, The Symmetric Group, Wadsworth & Brooks/Cole, Pacific Grove, 1991; 2nd Edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York, 2001.
28. M. Saks, "Dilworth numbers, incidence maps and product partial orders," SIAM J. Algebraic Discrete Methods 1 (1980), 211-215.
29. M. Saks, "Some sequences associated with combinatorial structures," Discrete Math. 59 (1986), 125-166.
30. C. Schensted, "Longest increasing and decreasing subsequences," Canad. J. Math. 13 (1961), 179-191.
31. N. Spaltenstein, "On the fixed point set of a unipotent transformation on the flag manifold," Nederl. Akad. Wetensch. Indag. Math. 38 (1976), 452-458 (same as: Nederl. Akad. Wetensh. Proc. Ser. A 79).
32. N. Spaltenstein, "On the fixed point set of a unipotent transformation on the flag manifold," Nederl. Akad. Wetensch. Indag. Math. 38 (1976), 452-458 (same as: Nederl. Akad. Wetensh. Proc. Ser. A 79).
33. T. A. Springer, "Some results on algebraic groups with involutions," in Algebraic Groups and Related Topics, Advanced Studies in Pure Mathematics, Vol. 6, Kyoto/Nagoya, 1983, Kinokuniya, Tokyo, 1985, pp. 525-543.
34. T. A. Springer, "Schubert varieties and generalizations," in Representation Theories and Algebraic Geometry, Montréal, 1997, A. Broer and A. Daigneault (Eds.), Kluwer, Dortrecht, 1998, pp. 413-440.
35. R. Steinberg, "An occurrence of the Robinson-Schensted correspondence," J. Algebra 113 (1988), 523-528.
36. S. Sundaram, "On the combinatorics of representations of Sp(2n, ℂ)," Ph.D. Thesis, M.I.T., 1986.
37. S. Sundaram, "The Cauchy identity for Sp(2n)," J. Combin. Theory Ser. A 53 (1990), 209-238.
38. I. Terada, "A Robinson-Schensted-type correspondence for a dual pair on spinors," J. Combin. Theory Ser. A 63 (1993), 90-109.
39. G.P. Tesler, "Semi-primary lattices and tableau algorithms," Ph.D. Thesis, M.I.T., 1995.
40. P.E. Trapa, "Generalized Robinson-Schensted algorithms for real groups," Internat. Math. Res. Notices 1999 (1999), 803-832.
41. M.A.A. van Leeuwen, "A Robinson-Schensted algorithm in the geometry of flags for classical groups," Ph.D. Thesis, De Rijksuniversiteit te Utrecht, 1989.