Permutation modules are fundamental in the representation theory of symmetric groups Sn and their corresponding Iwahori–Hecke algebras H = H (Sn). We find an explicit combinatorial basis for the annihilator of a permutation module in the “integral” case — showing that it is a cell ideal in G.E. Murphy’s cell structure of H . The same result holds whenever H is semisimple, but may fail in the no...

Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a th...

Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we review the recent progress in constructing these theories and discuss some of their possible applications. Based on talks by B. de Wit and H. Nicolai at the ...

0. Introduction 3 0.1. Reduced decompositions 4 0.2. Affine exponents 7 0.3. Non–semisimple polynomials 12 0.4. Expected applications 17 1. Affine Weyl groups 21 1.1. Affine roots 22 1.2. The length on Ŵ 24 1.3. Reduction modulo W 29 1.4. Partial ordering on P 34 2. Reduced decompositions 37 2.1. Lambda–sequences 37 2.2. Coxeter transformations 39 2.3. Theorem about triples 42 2.4. Discussion 4...

In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideal...

In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra H via the categorical counterpart developed in a 2005 preprint. When H is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of H such that...

In an important sequence of papers, Halmos has developed the beautiful and significant theory of algebraic logic. The central mathematical object of this theory is the polyadic algebra, which incorporates in an axiomatic way the concepts of substitution, transformation, and quantification for the lower functional calculus. The beauty of the theory is revealed by the fact that the semantic compl...

Why is it so hard to prove the linearizability of Poisson structures with semisimple linear part? Conn published proofs about 15 years ago in a pair of papers [5][6] full of elaborate estimates. Except for the somewhat more conceptual reformulation by Desolneux-Moulis [9] in the smooth case, no simplification of Conn’s proofs has appeared. This is a mystery to me, because analogous theorems abo...