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Combinatorics Seminar: On statistic of irreducible components March 04, 2019 (12:10 PM PST - 01:00 PM PST)
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Location: UC Berkeley Math (Evans Hall 939)
Speaker(s) Nicolai Reshetikhin (University of California, Berkeley)
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For finite dimensional representations V1,…,VmV1,…,Vm of a simple finite dimensional Lie algebra gg consider the tensor product W=⊗mI=1V⊗NiiW=⊗I=1mVi⊗Ni. The first result, which will be presented in the talk, is the asymptotic of the multiplicity of an irreducible representation VλVλ with the highest weight λ in this tensor product when Ni=τi/ϵ,λ=ξ/ϵNi=τi/ϵ,λ=ξ/ϵ and ϵ→0ϵ→0. Then we will discuss the asymptotical distribution of irreducible components with respect to the character probability measure Prob(λ)=mλχVλ(et)χW(et)Prob(λ)=mλχVλ(et)χW(et). Here χV(et)χV(et) is the character of representation VVevaluated on etet where tt is an element of the Cartan subalgebra of the split real form of the Lie algebra gg. This is a joint work with O. Postnova.

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