ar X iv : m at h / 06 06 73 4 v 1 [ m at h . M G ] 2 8 Ju n 20 06 CODES IN SPHERICAL CAPS

ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE

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.

ar X iv : m at h / 06 06 27 5 v 1 [ m at h . A T ] 1 2 Ju n 20 06 MODULES IN MONOIDAL MODEL CATEGORIES

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

ar X iv : m at h / 06 06 31 2 v 1 [ m at h . A C ] 1 3 Ju n 20 06 ASYMPTOTIC BEHAVIOR OF MULTIGRADED REGULARITY

Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.