ar X iv : m at h / 06 01 47 2 v 1 [ m at h . Q A ] 1 9 Ja n 20 06 REPRESENTATIONS OF QUANTUM GROUPS DEFINED OVER COMMUTATIVE RINGS II

ar X iv : m at h / 06 01 26 6 v 1 [ m at h . Q A ] 1 1 Ja n 20 06 ON THE HECKE ALGEBRAS AND THE COLORED HOMFLY POLYNOMIAL

Abstract. The colored HOMFLY polynomial is the quantum invariant of oriented links in S associated with irreducible representations of the quantum group Uq(slN). In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The te...

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : m at h / 06 01 47 5 v 2 [ m at h . PR ] 2 9 Ja n 20 07 Isoperimetry between exponential and Gaussian

We study the isoperimetric problem for product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the isoperimetric problem.

ar X iv : m at h / 05 01 45 4 v 2 [ m at h . A G ] 1 2 Ja n 20 06 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES

We calculate the dimension of the locus of Jacobian elliptic surfaces over P with given Picard number, in the corresponding moduli space.

ar X iv : m at h / 03 06 32 1 v 1 [ m at h . Q A ] 2 3 Ju n 20 03 Representations of U ε ( g ) over spherical orbits . II

Let Uε(g) be the simply connected quantized enveloping algebra associated to an exceptional simple Lie algebra g at the roots of unity. The De Concini-Kac-Procesi conjecture on the dimension of the irreducible representations of Uε(g) is proved for representations corresponding to the spherical conjugacy classes of the simply connected group with Lie algebra g.