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

Released on by Jonah Blasiak
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  • Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem Book Detail

  • Author : Jonah Blasiak
  • Release Date : 2015-04-09
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 176
  • ISBN 13 : 1470410117
  • File Size : 31,31 MB
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Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by Jonah Blasiak PDF Summary

Book Description: 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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Geometry and Complexity Theory

Geometry and Complexity Theory

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This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.