Let GM be either the orthogonal group OM , or the symplectic group SpM over the complex field; in the latter case the non-negative integer M has to be even. Classically, the irreducible finite-dimensional representations of the group GM are labeled by partitions μ = (μ1, μ2 , . . .) such that μ ′ 1+μ ′ 2 6 M in the case GM = OM , or 2μ ′ 1 6 M in the case GM = SpM . Here μ ′ = (μ ′ 1, μ ′ 2 , ....

We construct the polynomial induction functor, which is right adjoint to restriction functor from category of representations a general linear group its Weyl group. This construction leads representation-theoretic proof Littlewood’s plethystic formula for multiplicity an irreducible representation symmetric in such restriction. The unimodality certain bipartite partition functions follows.

Suppose P is a parabolic subgroup of G with Levi factor M and σ = ⊗σv a cuspidal representation ofM(A). Then Ind σ = ⊗vInd σv is a representation of G(A) which may not be irreducible, and may not even have a finite composition series. As usual an irreducible subquotient of this representation is said to be a constituent of it. For almost all v, Ind σv has exactly one constituent π ◦ v containin...

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...

A 2-category was introduced in math.QA/0803.3652 that categorifies Lusztig’s integral version of quantum sl(2). Here we construct for each positive integer N a representation of this 2-category using the equivariant cohomology of iterated flag varieties. This representation categorifies the irreducible (N + 1)-dimensional representation of quantum sl(2).

We consider the string, like point particles and branes, to be an irreducible representation of semi-direct product Cartan involution invariant subalgebra [Formula: see text] its vector representation. show that preserves string charges, little algebra, is essentially Borel text]. also known physical states carry a parts this algebra.

We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n − 1, 1) which s...

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...

Let be weighted Bergman space on a bounded symmetric domain . It has analytic continuation in the weight and for in the so-called Wallach set still forms unitary irreducible (projective) representations of . We give the irreducible decomposition of the tensor product of the representation for any two unitary weights and we find the highest weight vectors of the irreducible components. We find a...