A.Varchenko
Reality property of discrete Wronski map with imaginary step.
Tue, 03/01/2011 - 16:01 — SomNambulAuthors: E. Mukhin, V. Tarasov, A.Varchenko
Subjects: Quantum Algebra
AbstractFor a set of quasi-exponentials with real exponents, we consider the discrete
Wronskian (also known as Casorati determinant) with pure imaginary step 2h. We
prove that if the coefficients of the discrete Wronskian are real and for every
its roots the imaginary part is at most |h|, then the complex span of this set
of quasi-exponentials has a basis consisting of quasi-exponentials with real
coefficients. This result is a generalization of the statement of the B. and M.
Shapiro conjecture on spaces of polynomials. The proof is based on the Bethe
ansatz for the XXX model.- 17 comments
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Cohomology of a flag variety as a Bethe algebra.
Mon, 02/07/2011 - 16:01 — SomNambulAuthors: A.Varchenko, R.Rimanyi, V.Schechtman, V.Tarasov
Subjects: Quantum Algebra
AbstractWe interpret the GL_n equivariant cohomology of a partial flag variety of
flags of length N in \C^n as the Bethe algebra of a suitable gl_N[t] module
associated with the tensor power (\C^N)^{\otimes n}.- 3 comments
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Bethe algebra of the gl_{N+1} Gaudin model and algebra of functions on the critical set of the master function.
Tue, 10/27/2009 - 16:01 — SomNambulAuthors: E. Mukhin, V. Tarasov, A.Varchenko
Subjects: Quantum Algebra
AbstractConsider a tensor product of finite-dimensional irreducible gl_{N+1}-modules
and its decomposition into irreducible modules. The gl_{N+1} Gaudin model
assigns to each multiplicity space of that decomposition a commutative (Bethe)
algebra of linear operators acting on the multiplicity space. The Bethe ansatz
method is a method to find eigenvectors and eigenvalues of the Bethe algebra.
One starts with a critical point of a suitable (master) function and constructs
an eigenvector of the Bethe algebra.
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