Tensor product varieties and crystals. GL case

Preprint English OPEN
Malkin, Anton;
(2001)
  • Subject: Mathematics - Combinatorics | Mathematics - Algebraic Geometry | Mathematics - Representation Theory
    arxiv: Mathematics::Representation Theory

The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain t... View more
  • References (16)
    16 references, page 1 of 2

    [BM83] W. Borho and R. MacPherson, Partial resolutions of nilpotent varieties, Analysis and topology on singular spaces, II, III (Luminy, 1981), Soc. Math. France, Paris, 1983, pp. 23-74.

    [Gin91] V. Ginzburg, Lagrangian construction of the enveloping algebra U (sln), C. R. Acad. Sci. Paris S´er. I Math. 312 (1991), no. 12, 907-912.

    [GL92] I. Grojnowski and G. Lusztig, On bases of irreducible representations of quantum gln, Kazhdan-Lusztig theory and related topics (Chicago, IL, 1989), AMS, Providence, RI, 1992, pp. 167-174.

    [Hal59] P. Hall, The algebra of partitions, Proc. 4th Canadian Math. Congress (Banff), University of Toronto Press, 1959, pp. 147-159.

    [Jos95] A. Joseph, Quantum groups and their primitive ideals, Springer-Verlag, Berlin, 1995.

    [Kas90] M. Kashiwara, Crystalizing the q-analogue of universal enveloping algebras, Comm. Math. Phys. 133 (1990), no. 2, 249-260.

    [Kas91] M. Kashiwara, On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), no. 2, 465-516.

    [Kas94] M. Kashiwara, Crystal bases of modified quantized enveloping algebra, Duke Math. J. 73 (1994), no. 2, 383-413.

    [KS97] M. Kashiwara and Y. Saito, Geometric construction of crystal bases, Duke Math. J. 89 (1997), no. 1, 9-36.

    [Lus91] G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), no. 2, 365-421.

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