In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of the representation of a finite Coxeter group W on the pth graded piece of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W . Our refined conjecture relates the character of W on the pth graded piece of its Orlik-Solomon algebra with the ...

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...

Let G be a connected linear algebraic group over an algebraically closed field of characteristic zero. Then the Brauer group of G is shown to be C X (Q/Z)<n) where C is finite and n = d(d l)/2, with d the Z-Ta.nk of the character group of G. In particular, a linear torus of dimension d has Brauer group (Q/Z)(n) with n as above. In [6], B. Iversen calculated the Brauer group of a connected, char...

Sinhala characters used in the Sinhala script by over 70% of the 18 million population in Sri Lanka, have been descended from the ancient Brahmi script. The Sinhala alphabet consists of vowels and consonants and the consonants are modified using modifier symbols to give the required vocal sounds. In the process of developing an OCR for the Sinhala script, characters are initially recognised thr...

Characters, like other articulated objects and structures, are typically simulated using articulated dynamics algorithms. There are efficient linear-time algorithms for the simulation of open-chain articulated bodies, but complexity grows notably under additional constraints such as joint limits, loops or contact, or if the bodies undergo stiff joint forces. This paper presents a linear-time al...

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...

Given a word W in the free group on 2 letters F2, Horowitz showed that the special linear character of W is an integer polynomial in the 3 characters of the basic words of F2. Special linear characters are defined via the trace of their representations, and the polynomial character of an arbitrary W can be found by application of certain “trace relations”, which allow one to write the character...

Let G be a connected reductive Lie group with a relatively compact Cartan subgroup. Then it has relative discrete series representations. The main result of this paper is a formula expressing relative discrete series characters on G as “lifts” of relative discrete series characters on smaller groups called two-structure groups for G. The two-structure groups are connected reductive Lie groups w...