ar X iv : m at h - ph / 0 11 10 40 v 1 2 1 N ov 2 00 1 A Frame Bundle Generalization of Multisymplectic

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : h ep - p h / 00 11 11 7 v 1 8 N ov 2 00 0 1 ( Mis ) Understanding the Atmospheric Neutrino Anomaly

ar X iv : m at h - ph / 0 11 10 07 v 1 5 N ov 2 00 1 FREDHOLM DETERMINANTS , JIMBO - MIWA - UENO TAU - FUNCTIONS , AND REPRESENTATION THEORY

The authors show that a wide class of Fredholm determinants arising in the representation theory of " big " groups such as the infinite–dimensional unitary group, solve Painlevé equations. Their methods are based on the theory of integrable operators and the theory of Riemann–Hilbert problems.

ar X iv : m at h - ph / 0 40 40 45 v 2 2 5 N ov 2 00 4 On the refined 3 - enumeration of alternating sign matrices

An explicit expression for the numbers A(n, r; 3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n, r; 3)'s are represented as 1-fold sums which can also be written in terms of terminating 4 F 3 series of argument 1/4.

ar X iv : m at h - ph / 0 51 10 53 v 1 1 6 N ov 2 00 5 Normal bundles to Laufer rational curves in local

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points. MSC: 14D15, 14H45, 83E30 PACS: 02....