Related papers: Signature Characters for A_2 and B_2
Let $G={\rm GL}_n$ be the general linear group over an algebraically closed field $k$, let $\mathfrak g=\mathfrak gl_n$ be its Lie algebra and let $U$ be the subgroup of $G$ which consists of the upper uni-triangular matrices. Let…
The character of every irreducible finite-dimensional representation of a simple Lie algebra has the highest weight property. The invariance of the character under the action of the Weyl group W implies that there is a similar "extremal…
This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera…
The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and…
An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power…
We study the highest weight and continuous tensor product representations of q-deformed Lie algebras through the mappings of a manifold into a locally compact group. As an example the highest weight representation of the q-deformed algebra…
We determine the irreducible representations of simple Lie algebras with maximum weight multiplicity 2.
The characters of irreducible finite dimensional representations of compact simple Lie group G are invariant with respect to the action of the Weyl group W(G) of G. The defining property of the new character-like functions ("hybrid…
We establish an irreducibility property for the characters of finite dimensional, irreducible representations of simple Lie algebras (or simple algebraic groups) over the complex numbers, i.e., that the characters of irreducible…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
Determining whether an irreducible representation of a group (or $*$-algebra) admits a non-degenerate invariant, positive-definite Hermitian form is an important problem in representation theory. In this paper, we study a related notion:…
In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules $L$ over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $\mathfrak{g}$. The problems…
Let g_A (respectively, g_A(\mu)) be the graded multi-loop Lie algebra (respectively graded twisted multi-loop Lie algebra)" associated with the simple finite dimensional Lie algebra g over the complex field C. In this paper, we prove that…
The Iwahori-Hecke algebra of type A acts on tensor product space of the natural representation of the quantum superalgebra U_q(gl(m,n)). We show this action of the Hecke algebra and the action of U_q(gl(m,n)) on the same space determine…
We explore combinatorial formulas for deformations of highest weight characters of the odd orthogonal group $SO(2n+1)$. Our goal is to represent these deformations of characters as partition functions of statistical mechanical models -- in…
We give a characterization for the binary linear constant weight codes by using the symmetric difference of the supports of the codewords. This characterization gives a correspondence between the set of binary linear constant weight codes…
We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the…
We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite affine Cartan matrix. We give explicit…
We study the structure of the finite-dimensional representations of $\mathfrak{sl}_2[t]$, the current Lie algebra type of $A_1$, which are obtained by taking tensor products of special Demazure modules. We show that these representations…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.