In their fundamental studies of the finite dimensional representations of associative algebras, Artin and Procesi proved that the primitive ideals corresponding to irreducible n-dimensional representations (for fixed n, over an algebraically closed field) can be homeomorphically parameterized by a locally closed subset of the maximal spectrum of a suitably chosen affine commutative trace ring. ...

Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of H. Here, we give a quick proof of this result, computing the index and kerne...

In this paper, we study the restriction of an irreducible unitary representation π of the universal covering S̃p2n(R) to a Heisenberg maximal parabolic group P̃ . We prove that if π|P̃ is irreducible, then π must be a highest weight module or a lowest weight module. This is in sharp constrast with the GLn(R) case. In addition, we show that for a unitary highest or lowest weight module, π|P̃ decompo...

This paper is concerned with actions of finite hypergroups on sets. After introducing the definitions in the first section, we use the notion of ‘maximal actions’ to characterise those hypergroups which arise from association schemes, introduce the natural sub-class of *-actions of a hypergroup and introduce a geometric condition for the existence of *-actions of a Hermitian hypergroup. Followi...

We determine all nite groups G which admit a subgroup K of index p a ; p a prime, under the assumption that G has an irreducible and faithful GF (p)-module of dimension at most a. As an application to the theory of permutation groups we determine the maximal transitive subgroups of the primitive aane permutation groups.

Let C be a nonsingular irreducible projective curve of genus g ≥ 2 defined over the complex numbers. Suppose that 1 ≤ n ′ ≤ n − 1 and n ′ d − nd ′ = n ′ (n − n ′)(g − 1). It is known that, for the general vector bundle E of rank n and degree d, the maximal degree of a subbundle of E of rank n ′ is d ′ and that there are finitely many such subbundles. We obtain a formula for the number of these ...

We study the polynomial representation of the rational Cherednik algebra of type An−1 with generic parameter in characteristic p for p | n. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic p analogues...

Let M be a closed, irreducible, genus two 3–manifold, and F a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in M . Then each component manifold Mi of M − F has handle number one, i.e. admits a Heegaard splitting obtained by attaching a single 1–handle to one or two components of ∂Mi. This result also holds for a decomposition of M along a maximal ...

A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this space and ideals in the AF algebra. Some connections with nest representations and nestprimitive ideals are also described.

Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field k of characteristic p > 0, T a maximal torus of G and B a Borel subgroup containing T . Each weight in X(T ) determines a line bundle on the flag varietyG/B. It turns out that cohomology of the line bundle is isomorphic to the derived functor of the induction functors from the category of B-m...