Sum formulas for reductive algebraic groups

Sum Formulas for Reductive Algebraic Groups Henning Haahr Andersen and Upendra Kulkarni

Let V be aWeyl module either for a reductive algebraic group G or for the corresponding quantum group Uq. If G is defined over a field of positive characteristic p, respectively if q is a primitive l’th root of unity (in an arbitrary field) then V has a Jantzen filtration V = V 0 ⊃ V 1 · · · ⊃ V r = 0. The sum of the positive terms in this filtration satisfies a well known sum formula. If T den...

Computing in Unipotent and Reductive Algebraic Groups

The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup of a split reductive group and show how this improves computation in the reductive group itself.

On a Class of Double Cosets in Reductive Algebraic Groups

We study a class of double coset spaces RA\G1 × G2/RC , where G1 and G2 are connected reductive algebraic groups, and RA and RC are certain spherical subgroups of G1×G2 obtained by “identifying” Levi factors of parabolic subgroups in G1 and G2. Such double cosets naturally appear in the symplectic leaf decompositions of Poisson homogeneous spaces of complex reductive groups with the Belavin–Dri...

Reductive Groups

Representations of Reductive Groups

This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...