منابع مشابه
Hall-Littlewood functions at roots of unity
Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.
متن کاملTHE q–CHARACTERS AT ROOTS OF UNITY
We consider various specializations of the untwisted quantum affine algebras at roots of unity. We define and study the q–characters of their finite-dimensional representations.
متن کاملQuantum Affine Algebras at Roots of Unity
Let Uq(ĝ) be the quantized universal enveloping algebra of the affine Lie algebra ĝ associated to a finite-dimensional complex simple Lie algebra g, and let U res q (ĝ) be the C[q, q−1]-subalgebra of Uq(ĝ) generated by the q-divided powers of the Chevalley generators. Let U res (ĝ) be the Hopf algebra obtained from U res q (ĝ) by specialising q to a non-zero complex number of odd order. We clas...
متن کاملOn Hadamard Matrices at Roots of Unity
Abstract. We study Hadamard matrices of order n, formed by l-th roots of unity. A main problem is to find the allowed values of (n, l), and we discuss here the following statement: for l = pa 1 . . . pa s we must have n ∈ p1+. . .+psN. For s = 1 this is a previously known result, for s = 2, 3 this is a result that we prove in this paper, and for s ≥ 4 this is a conjecture that we raise. We pres...
متن کاملCompleting Bethe’s equations at roots of unity
In a previous paper we demonstrated that Bethe’s equations are not sufficient to specify the eigenvectors of the XXZ model at roots of unity for states where the Hamiltonian has degenerate eigenvalues. We here find the equations which will complete the specification of the eigenvectors in these degenerate cases and present evidence that the sl2 loop algebra symmetry is sufficiently powerful to ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/10/008