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This article is cited in 17 scientific papers (total in 17 papers)
Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel
Evgeny Mukhina, Vitaly Tarasovab, Alexander Varchenkoc a Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 North Blackford St, Indianapolis, IN 46202-3216, USA
b St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia
c Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA
Abstract:
Let $M$ be the tensor product of finite-dimensional polynomial evaluation $Y(\mathfrak{gl}_N)$-modules. Consider the universal difference operator $\mathfrak D=\sum\limits_{k=0}^N (-1)^k\mathfrak T_k(u) e^{-k\partial _u }$ whose coefficients $\mathfrak T_k(u)\colon M\to M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $\mathfrak D f=0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D=\sum\limits_{k=0}^N (-1)^k\mathcal S_k(u)\partial_u^{N-k}$ whose coefficients
$\mathcal S_k(u)\colon\mathcal M\to\mathcal M$ are the Gaudin transfer matrices associated with the
tensor product $\mathcal M$ of finite-dimensional polynomial evaluation $\mathfrak{gl}_N[x]$-modules.
Keywords:
Gaudin model; XXX model; universal differential operator.
Received: March 28, 2007; Published online April 25, 2007
Citation:
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel”, SIGMA, 3 (2007), 060, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma186 https://www.mathnet.ru/eng/sigma/v3/p60
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