Abstract. Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function obtained from Blattner’s formula. This expression involves a product with a character of an irreducible finite dimensional representation of K and...

1.1. Formulations of the main problems. Let G be a simply connected complex semisimple Lie group of rank r with a fixed Borel subgroup B and a maximal torus H ⊂ B. Let W = NormG(H)/H be the Weyl group of G. The generalized flag manifold G/B can be decomposed into the disjoint union of Schubert cells X w = (BwB)/B, for w ∈ W . To any weight γ that is W -conjugate to some fundamental weight of G,...

The lattices of eightand ten-dimensional Euclidean space with irreducible automorphism group or, equivalently, the conjugacy classes of these groups in GL„(Z) for n = 8, 10, are classified in this paper. The number of types is 52 in the case n = 8 , and 47 in the case n = 10. As a consequence of this classification one has 26, resp. 46, conjugacy classes of maximal finite irreducible subgroups ...

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...

In this paper we study the nest representations ρ : A −→ Alg N of a strongly maximal TAF algebra A, whose ranges contain non-zero compact operators. We introduce a particular class of such representations, the essential nest representations , and we show that their kernels coincide with the completely meet irreducible ideals. From this we deduce that there exist enough contractive nest represen...

In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen-Macaulay curves in P. We give a sharp upper bound for the maximum number of points of intersection of two irreducible arithmetically Cohen-Macaulay curves Ct and Ct−r in P 3 defined by the maximal minors of a t× (t+ 1), resp. (t− r)× (t − r + 1), matrix with linear entries...

Suppose G is a real reductive Lie group, with maximal compact subgroup K. The representation theory of K is well-understood and well-behaved: K̂ is a countable discrete set consisting of finite-dimensional representations (δ, Eδ). If (π, V ) is a quasisimple irreducible representation of G, HarishChandra proved that each irreducible representation of K appears at most finitely often in V ; so th...

In this paper we study complex representations of the factorpower FP(G,M) of a finite group G acting on a finite set M . This includes the finite monoid FP+(Sn), which can be seen as a kind of a “balanced” generalization of the symmetric group Sn inside the semigroup of all binary relations. We describe all irreducible representations of FP(G,M) and relate them to irreducible representations of...

Let G be a connected reductive group defined over an algebraically closed base field of characteristic p ≥ 0, let B ⊆ G be a Borel subgroup, and let X be a G-variety. We denote the (finite) set of closed B-invariant irreducible subvarieties of X that are of maximal complexity by B0(X). The first named author has shown that for p = 0 there is a natural action of the Weyl group W on B0(X) and con...