Projective characters of exceptional Weyl groups

On characters of Weyl groups

In this note a combinatorial character formula related to the symmetric group is generalized to an arbitrary finite Weyl group. 1 The Case of the Symmetric Group The length l(π) of a permutation π ∈ Sn is the number of inversions of π, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). For any permutation π ∈ Sn let m(π) be defined as (1) m(π) := 

On Pointed Hopf Algebras with Weyl Groups of Exceptional Type

All −1-type pointed Hopf algebras with Weyl groups of exceptional type are found. It is proved that every non −1-type pointed Hopf algebra is infinite dimensional. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Weyl group.

Computational Aspects of Root Systems, Coxeter Groups, and Weyl Characters

Averages over Classical Compact Lie Groups and Weyl Characters

Abstract. We compute EG( ∏ i tr(g i)), where G = Sp(2n) or SO(m) (m = 2n, 2n + 1) with Haar measure. This was first obtained by Diaconis and Shahshahani [9], but our proof is more selfcontained and gives a combinatorial description for the answer. We also consider how averages of general symmetric functions EGΦn are affected when we introduce a Weyl character χλ into the integrand. We show that...

Enumerating Excedances with Linear Characters in Classical Weyl Groups

Several signed excedance-type statistics have nice formulae when summed over the symmetric group and over the hyperoctahedral group. Motivated by these, we consider sums of the form fχ,n(q) = ∑ w∈W χ(w)q exc(w) where W is a classical Weyl group of rank n, χ is a non-trivial one-dimensional character of W , and exc(w) is the excedance statistic of w. We give formulae for these sums in a more gen...