Alexander Varchenko

activity

20032005

most citedMultiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture

11 citations · 25 across the 10 of their papers we have counts for

collaborators

Showing 2004Show all

5 papers · 1 filter

math.QA2004

Selberg Integrals

Alexander Varchenko

The paper is written for Kluwer's Encyclopaedia of Mathematics.

math.QA2004★ 4 cited

Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model

Alexander Varchenko

We show that the Shapovalov norm of a Bethe vector in the Gaudin model is equal to the Hessian of the logarithm of the corresponding master function at the corresponding isolated c…

math.CO2004★ 2 cited

Combinatorics of rational functions and Poincare-Birkhoff-Witt expansions of the canonical U(n-)-valued differential form

R. Rimanyi, L. Stevens, A. Varchenko

We study the canonical U(n-)-valued differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of KZ-type dif…

math.QA2004★ 2 cited

Norm of a Bethe Vector and the Hessian of the Master Function

Evgeny Mukhin, Alexander Varchenko

We show that the Bethe vectors are non-zero vectors in the sl_{r+1} Gaudin model. Moreover, we show that the norm of a Bethe vector is equal to the Hessian of the corresponding mas…

math.GT2004

Finite order invariants for $(n, 2)$ -torus knots and the curve $Y^{2} = X^{3} + X^{2}$

Svetlana Tyurina, Alexander Varchenko

We describe the algebra of finite order invariants on the set of all $(n, 2)$ -torus knots.

Selberg Integrals

Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model

Combinatorics of rational functions and Poincare-Birkhoff-Witt expansions of the canonical U(n-)-valued differential form

Norm of a Bethe Vector and the Hessian of the Master Function

Finite order invariants for (n,2)-torus knots and the curve Y2=X3+X2

Finite order invariants for $(n, 2)$ -torus knots and the curve $Y^{2} = X^{3} + X^{2}$