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Spaces of quasi-exponentials and representations of the Yangian Y(gl_N) | | E. Mukhin
; V. Tarasov
; A. Varchenko
; | | Date: |
7 Mar 2013 | | Abstract: | We consider a tensor product $V(b)= otimes_{i=1}^nC^N(b_i)$ of the Yangian
$Y(gl_N)$ evaluation vector representations. We consider the action of the
commutative Bethe subalgebra $B^q subset Y(gl_N)$ on a $gl_N$-weight subspace
$V(b)_lambda subset V(b)$ of weight $lambda$. Here the Bethe algebra depends
on the parameters $q=(q_1,...,q_N)$. We identify the $B^q$-module
$V(b)_lambda$ with the regular representation of the algebra of functions on a
fiber of a suitable discrete Wronski map. If $q=(1,...,1)$, we study the action
of $B^{q=1}$ on a space $V(b)^{sing}_lambda$ of singular vectors of a certain
weight. Again, we identify the $B^{q=1}$-module $V(b)^{sing}_lambda$ with the
regular representation of the algebra of functions on a fiber of another
suitable discrete Wronski map.
These results we announced earlier in relation with a description of the
quantum equivariant cohomology of the cotangent bundle of a partial flag
variety and a description of commutative subalgebras of the group algebra of a
symmetric group. | | Source: | arXiv, 1303.1578 | | Services: | Forum | Review | PDF | Favorites | |
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