Mauro Costantini

Multiparameter quantum function algebra at roots of 1

We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De Concini-Lyubashenko in the standard quantum case.

A classification of unipotent spherical conjugacy classes in bad characteristic

Let G be a simple algebraic group over an algebraically closed fiel k of bad characteristic. We classify the spherical unipotent conjugacy cl asses ofG. We also show that if the characteristic of k is 2, then the fixed point subgroup of every involutorial auto morphism (involution) ofG is a spherical subgroup of G.

On Lusztig's map for spherical unipotent conjugacy classes

We provide an alternative description of the restriction to spherical unipotent conjugacy classes, of Lusztigs map Psi from the set of unipotent conjugacy classes in a connected reductive algebraic group to the set of conjugacy classes of its Weyl group. For irreducible root systems, we analyze the image of this restricted map and we prove that a conjugacy class in a finite Weyl group has a unique maximal length element if and only if it has a maximum.

On Finite Groups in Which Cyclic Subgroups of the Same Order are Conjugate

We consider finite groups G for which any two cyclic subgroups of the same order are conjugate in G. We prove various structure results and, in particular, that any such group has at most one non-abelian composition factor, and this is isomorphic to PSL(2, p m ), with m odd if p is odd, or to Sz(22m+1), or to one of the sporadic groups M 11, M 23, or J 1.

On the Quantum Function Algebra at Roots of One

Abstract In this note we show that certain properties of the quantum function algebra at roots of unity hold over any algebraically closed field of characteristic zero.

Simple modules over the multiparameter quantum function algebra at roots of 1

We construct essentially all the irreducible modules for the multiparameter quantum function algebraFɛφ[G], whereG is a simple simply connected complex algebraic group, and ɛ is a root of unity.

The lattice automorphisms of simple algebraic groups over\(\bar F_2 \)

AbstractWe prove that if u is a unipotent element of a connected reductive algebraic group G over

SPHERICAL ORBITS AND REPRESENTATIONS OF Uε(g)

\bar F_2