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Search Results: 1 - 10 of 485 matches for " Andras Szenes "
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The combinatorics of the Verlinde formulas
Andras Szenes
Physics , 1994,
Abstract: A residue formula is given for the Verlinde formula, which allows one to calculate its coefficients as a polynomial in the level and connects it to the Riemann-Roch formula on the moduli space of vector bundles on a curve.
A residue theorem for rational trigonometric sums and Verlinde's formula
Andras Szenes
Mathematics , 2001,
Abstract: We present a compact formula computing rational trigonometric sums. E. Verlinde's expression for the dimension of conformal blocks in WZW theory is an example of such a sum. As an application, we show that a formula of Bismut and Labourie for the Riemann-Roch numbers of moduli spaces of flat connections on a Riemann surface coincides with Verlinde's expression.
Exceptional points for Lebesgue's density theorem on the real line
Andras Szenes
Mathematics , 2007,
Abstract: For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither zero nor one. We quantify this statement, following work by V. Kolyada, and obtain the unexpected result that there is always a point where the upper and the lower densities are closer to 1/2 than to zero or one. The method of proof uses a combinatorial restatement of the problem.
Periodicity of Y-systems and flat connections
Andras Szenes
Mathematics , 2006,
Abstract: We give a proof of the periodicity of Zamolodchikov's Y-systems in the AxA case using a novel interpretation of the system as a condition of flatness of a connection on a certain graph.
Iterated Residues and Multiple Bernoulli Polynomials
Andras Szenes
Mathematics , 1997,
Abstract: We describe an effective method for calculating certain infinite sums, generalizations of the classical Bernoulli polynomials. As shown by Edward Witten in his papers on two-dimensional gauge theories, the correlation functions of two-dimensional topological Yang-Mills theory (or intersection numbers on moduli spaces of flat connections) can be given in the form of such infinite sums. Thus, in particular, our results give finite expressions for these correlation functions in the case of arbitrary compact structure groups G.
Crystal bases, dilogarithm identities and torsion in algebraic K-groups
Edward Frenkel,Andras Szenes
Physics , 1993,
Abstract: We give a new interpretation and proof of the dilogarithm identities, associated to the affine Kac-Moody algebra sl(2)^, using the path description of the corresponding crystal basis. We also discuss connections with algebraic K-theory.
Dilogarithm identities, q-difference equations and the Virasoro algebra
Edward Frenkel,Andras Szenes
Physics , 1992,
Abstract: We give a new proof of the dilogarithm identities, associated to the (2,2n+1) minimal models of the Virasoro algebra.
Thom polynomials of Morin singularities
Gergely Berczi,Andras Szenes
Mathematics , 2006,
Abstract: We prove a formula for Thom polynomials of Morin (or A_d) singularities in any codimension. We use a combination of the test-curve method of Porteous, and the localization methods in equivariant cohomology. Our formulas are independent of the codimension, and they are computationally efficient for d less than 7.
[Q,R]=0 and Kostant partition functions
Andras Szenes,Michele Vergne
Mathematics , 2010,
Abstract: On a polarized compact symplectic manifold endowed with an action of a compact Lie group, in analogy with geometric invariant theory, one can define the space of invariant functions of degree k. A central statement in symplectic geometry, the quantization commutes with reduction hypothesis, is equivalent to saying that the dimension of these invariant functions depends polynomially on k. This statement was proved by Meinrenken and Sjamaar under positivity conditions. In this paper, we give a new proof of this polynomiality property. The proof is based on a study of the Atiyah-Bott fixed point formula from the point of view of the theory of partition functions, and a technique for localizing positivity.
Thermodynamic Bethe Ansatz and Dilogarithm Identities I
Edward Frenkel,Andras Szenes
Mathematics , 1995,
Abstract: We consider the (A_n,A_1) Y-system arising in the Thermodynamic Bethe Ansatz. We prove the periodicity of solutions of this Y-system conjectured by Al.B. Zamolodchikov, and the dilogarithm identities conjectured by F. Gliozzi and R. Tateo.
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