A Bethe Ansatz for Symmetric Groups

Details A Bethe Ansatz for Symmetric Groups A Bethe Ansatz for Symmetric Groups

2010-03-02

arxiv.org/abs/1003.0490v1

Mathematics

Representation Theory

11 pages

Scientific paper

We examine the commuting elements $\theta_i=\sum_{j\neq i} \frac{s_{ij}}{z_i-z_j}$, $z_i\neq z_j$, $s_{ij}$ the transposition swapping $i$ and $j$, and we study their actions on irreducible $S_n$ representations. By applying Schur-Weyl duality to the results of \cite{RV:QuasiKZ}, we establish a Bethe Ansatz for these operators which yields joint eigenvectors for each critical point of a master function. By examining the asymptotics of the critical points, we establish a combinatorial description (up to monodromy) of the critical points and show that, generically, the Bethe vectors span the irreducible $S_n$ representations.

Affiliated with

Also associated with

No associations

Rating

A Bethe Ansatz for Symmetric Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Bethe Ansatz for Symmetric Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Bethe Ansatz for Symmetric Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-663301