COMBINATORICS OF THE ŝl 2 SPACES OF COINVARIANTS
نویسندگان
چکیده
We consider two types of quotients of the integrable modules of sl 2. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level k. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For k = 1, we give explicit formulas for the characters. We also present recursion relations satisfied by the characters and the monomial bases.
منابع مشابه
ar X iv : m at h - ph / 9 90 80 03 v 1 2 A ug 1 99 9 COMBINATORICS OF THE ŝl 2 SPACES OF COINVARIANTS
We consider two types of quotients of the integrable modules of sl2. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-k. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For k = 1, we give the explicit formulas for the characters. We also present recursion relations satisfied by the...
متن کاملSimple Conformal Algebras Generated by Jordan Algebras
1 Background and Motivation We start with an example of affine Kac-Moody algebras and the Virasoro algebra. In this talk, F will be a field with characteristic 0, and all the vector spaces are assumed over F. Denote by Z the ring of integers and by N the set of nonnegative integers. Let 2 ≤ n ∈ N. Set sl(n,F) = {A ∈ Mn×n(F) | tr A = 0}, (1.1) 〈A,B〉 = tr AB for A,B ∈ sl(n,F), (1.2) where Mn×n(F)...
متن کاملCombinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics
In [J. Haglund, A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants, Adv. Math. 227 (2011) 2092-2106], the study of the Hilbert series of diagonal coinvariants is linked to combinatorial objects called Tesler matrices. In this paper we use operator identities from Macdonald polynomial theory to give new and short proofs of some of these results. We also ...
متن کاملCommutative Quantum Current Operators, Semi-infinite Construction and Functional Models
We construct the commutative current operator x̄+(z) inside Uq(ŝl(2)). With this operator and the condition of quantum integrability on the quantum currents of Uq(ŝl(2)), we derive the quantization of the semiinfinite construction of integrable modules of ŝl(2) which has been previously obtained by means of the current operator e(z) of ŝl(2). The quantization of the functional models for ŝl(2) i...
متن کاملSPACES OF COINVARIANTS AND FUSION PRODUCT II. ŝl2 CHARACTER FORMULAS IN TERMS OF KOSTKA POLYNOMIALS
In this paper, we continue our study of the Hilbert polynomials of coinvariants begun in our previous work [FJKLM] (paper I). We describe the sln fusion products for symmetric tensor representations following the method of [FF], and show that their Hilbert polynomials are An−1-supernomials. We identify the fusion product of arbitrary irreducible sln-modules with the fusion product of their resc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001