publication . Preprint . 2001

Tensor product varieties and crystals. GL case

Malkin, Anton;
Open Access English
  • Published: 05 Mar 2001
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 tensor product multiplicity) is obtained.
arXiv: Mathematics::Representation Theory
free text keywords: Mathematics - Algebraic Geometry, Mathematics - Combinatorics, Mathematics - Representation Theory
Download from
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. [OpenAIRE]

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

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

[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. [OpenAIRE]

[LW54] S. Lang and A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819-827. [OpenAIRE]

[Mac95] I. Macdonald, Symmetric functions and Hall polynomials, second ed., The Clarendon Press Oxford University Press, New York, 1995.

[Mal01] A. Malkin, Tensor product varieties and crystals. ADE case., arXiv:math.AG/0103025 [Nak94] H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J. 76 (1994), no. 2, 365-416.

[Nak98] H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), no. 3, 515-560.

[Nak01] H. Nakajima, Quiver varieties and tensor products, arXiv:math.QA/0103008 [Spa82] N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Springer-Verlag, Berlin, 1982.

16 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue