|An algebraic-combinatorial approach to the Kronecker problem via quantum group representations|
du groupe Combinatoire Énumérative et Algébrique
|Date|| 2013-06-21 10:45-11:45|
|Titre||An algebraic-combinatorial approach to the Kronecker problem via quantum group representations |
|Résumé||In this talk, I will describe our on-going efforts towards an algebraic-combinatorial approach towards the Kronecker problem.
Consider the natural embedding of GLm(C) × GLn(C) into GLmn(C) via the Kronecker product. With respect to this embedding, a GLmn(C) irreducible representation Vλ(mn) splits into a direct sum of irreducible GLm(C) × GLn(C) representations:
Vλ(mn) = ⊕μ,ν χμ,νλ Vμ(m) ⊗ Vν(n)
The Kronecker problem is the problem of computing the multiplicity coefficents χμ,νλ.
We consider the quantized version of this problem and propose an approach to this problem via the theory of quantum groups and the crystal bases. I will talk about our initial results in this direction. The talk is based on joint work with Milind Sohoni and K. V. Subrahmanyam. |
|Orateur||Bharat Adsul |
|Url||Department of Computer Science and Engineering, Indian Institute of Technology Bombay, India |
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