Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem

Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem
Author :
Publisher : American Mathematical Soc.
Total Pages : 176
Release :
ISBN-10 : 9781470410117
ISBN-13 : 1470410117
Rating : 4/5 (117 Downloads)

Book Synopsis Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by : Jonah Blasiak

Download or read book Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem written by Jonah Blasiak and published by American Mathematical Soc.. This book was released on 2015-04-09 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.


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