Geometric Complexity Theory: Nonstandard Quantum Group for the Kronecker Problem: 4 - Brossura

Blasiak, Jonah; Mulmuley, Ketan D.; Sohoni, Milind

Brossura

ISBN 10: 1470410117 ISBN 13: 9781470410117

Casa editrice: Amer Mathematical Society, 2015

Riassunto

The Kronecker coefficient $g_{\lambda \mu \nu}$ is the multiplicity of the $GL(V)\times GL(W)$-irreducible $V_\lambda \otimes W_\mu$ in the restriction of the $GL(X)$-irreducible $X_\nu$ via the natural map $GL(V)\times GL(W) \to GL(V \otimes W)$, where $V, W$ are $\mathbb{C}$-vector spaces and $X = V \otimes W$. 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.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2015
• ISBN 10: 1470410117
• ISBN 13: 9781470410117
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 160
• Contatto del produttore: non disponibile