Matrix factorizations for nonaffine LG-models

We propose a natural definition of a category of matrix factorizations for nonaffine Landau-Ginzburg models. For any LG-model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the triangulated category of singularities of the corresponding fiber. We also show that this functor is an equivalence if the total space of the LG-model is smooth.Comment: 12 pages, minor corrections of TEX fil

Matrix integrals as Borel sums of Schur function expansions

The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of divergent sums over products of Schur functions in the two sequences of associated KP flow variables.Comment: PlainTex file. 8 pgs. Based on talk by J. Harnad at the workshop: Symmetry and Perturbation Theory 2002, Cala Gonoone (Sardinia), May 1-26, 2002. To appear in proceedings. (World Scientific, Singapore, eds. S. Abenda, G. Gaeta). Typographical correction made to formula (2.7) to include previously omitted powers of r and

Scalar products of symmetric functions and matrix integrals

We present relations between Hirota-type bilinear operators, scalar products on spaces of symmetric functions and integrals defining matrix model partition functions. Using the fermionic Fock space representation, a proof of the expansion of an associated class of KP and 2-Toda tau functions $\tau_{r,n}$ in a series of Schur functions generalizing the hypergeometric series is given and related to the scalar product formulae. It is shown how special cases of such $\tau$-functions may be identified as formal series expansions of partition functions. A closed form exapnsion of $\log \tau_{r,n}$ in terms of Schur functions is derived.Comment: LaTex file. 15 pgs. Based on talks by J. Harnad and A. Yu. Orlov at the workshop: Nonlinear evolution equations and dynamical systems 2002, Cadiz (Spain) June 9-16, 2002. To appear in proceedings. (Minor typographical corrections added, abstract expanded