as gl(V1)⊕ gl(V2)⊕ gl(V3)-modules. This yields a well-known reformulation of (2.1). Proposition A.1. If l(α) 6 dimV1 and l(β) 6 dimV2, then the Kronecker coefficient g(αβγ) is the multiplicity of V1(α)⊗ V2(β) in the gl(V1)⊕ gl(V2)-module (V1 ⊗ V2)(γ). If V is m-dimensional, then V (1) is the one-dimensional gl(V )-module carried by the trace map gl(V ) → C. It follows easily that V (n) ∼= V (1)...

We prove that the Robinson-Schensted-Knuth correspondence is a gl∞-crystal isomorphism between two realizations of the crystal graph of a generalized Verma module with respect to a maximal parabolic subalgebra of gl∞. A flagged version of the RSK correspondence is derived in a natural way by computing a Demazure crystal graph of a generalized Verma module. As an application, we discuss a relati...

For an algebraically closed base field of positive characteristic, an algorithm to construct some non-zero GL(n − 1)-high weight vectors of irreducible rational GL(n)-modules is suggested. It is based on the criterion proved in this paper for the existence of a set A such that Si,j(A)fμ,λ is a non-zero GL(n − 1)-high weight vector, where Si,j(A) is Kleshchev’s lowering operator and fμ,λ is a no...

We describe a Hopf algebraic approach to the Grothendieck ring of representations of subgroups Hπ of the general linear group GL(n) which stabilize a tensor of Young symmetry {π}. It turns out that the representation ring of the subgroup can be described as a Hopf algebra twist, with a 2-cocycle derived from the Cauchy kernel 2-cocycle using plethysms. Due to Schur-Weyl duality we also need to ...

Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V. The isomorphism between this group of actions and the symmetric group Sl enables the graded generalization of the Young symmet...

This paper proposes an elaboration of the Generative Lexicon (GL) in Pustejovsky (1995) based on a survey of BCCWJ (2009). I manually classified the Japanese NP1-no NP2 “NP1’s NP2” construction in accordance with semantic relations between the two nominals. The result indicates the need for the expansion of GL for computing the meaning of the NP1no NP2 construction by incorporating referential ...

By Langlands duality one usually understands a correspondence between automorphic representations of a reductive group G over the ring of adels of a field F , and homomorphisms from the Galois group Gal(F/F ) to the Langlands dual group GL. It was originally introduced in the case when F is a number field or the field of rational functions on a curve over a finite field [1]. Recently A. Beilins...

In this paper we consider several different methods to produce spanning sets for irreducible polynomial representations of GL(n,K) for an infinite field K, and we show how these spanning sets are related. The irreducible polynomial representations of GL(n,K) can be afforded by submodules L(λ) of Schur modules ∇(λ), indexed by partitions λ of positive integers r. Each ∇(λ) is a GL(n,K)-submodule...