7 A ug 2 00 8 Local analytic classification of q - difference

ar X iv : 0 80 2 . 42 23 v 1 [ m at h . Q A ] 2 8 Fe b 20 08 Local analytic classification of q - difference equations

3 Analytic classification of admissible q-difference modules 10 3.1 Generalities on q-difference modules . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Simple objects in the category of admissible q-difference modules . . . . . . . 11 3.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Analytic vs formal classification . . . . . . . . . . . . ...

A ug 2 00 5 A modular description of the K ( 2 ) - local sphere at the prime 3

Using degree N isogenies of elliptic curves, we produce a spectrum Q(N). This spectrum is built out of spectra related to tmf . At p = 3 we show that the K(2)local sphere is built out of Q(2) and its K(2)-local Spanier-Whitehead dual. This gives a conceptual reinterpretation a resolution of Goerss, Henn, Mahowald, and Rezk. AMS classification: Primary 55Q40, 55Q51, 55N34. Secondary 55S05, 14H52.

ar X iv : 0 90 8 . 10 44 v 1 [ m at h . Q A ] 7 A ug 2 00 9 Modular invariants for group - theoretical modular data

We classify indecomposable commutative separable (special Frobenius) algebras and their local modules in (untwisted) group-theoretical modular categories. This gives a description of modular invariants for grouptheoretical modular data. As a bi-product we provide an answer to the question when (and in how many ways) two group-theoretical modular categories are equivalent as ribbon categories.

03 7 v 1 1 8 A ug 2 00 0 The Q 2 - dependence of the Generalised Gerasimov - Drell - Hearn Integral for the Proton

ar X iv : 0 70 8 . 22 12 v 1 [ m at h . C O ] 1 6 A ug 2 00 7 Enumerative properties of NC ( B ) ( p , q )

We determine the rank generating function, the zeta polynomial and the Möbius function for the poset NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers.