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Tensor product varieties and crystals: $GL$ case


Author: Anton Malkin
Journal: Trans. Amer. Math. Soc. 354 (2002), 675-704
MSC (2000): Primary 20G99, 14M15
DOI: https://doi.org/10.1090/S0002-9947-01-02899-9
Published electronically: October 3, 2001
MathSciNet review: 1862563
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Abstract: A geometric theory of tensor product for $\mathfrak{gl}_{N}$-crystals is described. In particular, the role of Spaltenstein varieties in the tensor product is explained, and thus 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.


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Additional Information

Anton Malkin
Affiliation: Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283
Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Email: malkin@math.mit.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02899-9
Received by editor(s): March 7, 2001
Published electronically: October 3, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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