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We give a new interpretation of the chromatic polynomial of a simple graph $$G$$G in terms of the Kac–Moody Lie algebra $$\mathfrak {g}$$g with Dynkin diagram $$G$$G. We show that the chromatic… (More)

We consider a large class of series of symmetrizable Kac-Moody algebras (generically denoted X_n). This includes the classical series A_n as well as others like E_n whose members are of Indefinite… (More)

The principal objects studied in this note are Coxeter groups $W$ that are neither finite nor affine. A well known result of de la Harpe asserts that such groups have exponential growth. We consider… (More)

We introduce a generalization of the classical Hall-Littlewood and Kostka-Foulkes polynomials to all symmetrizable Kac-Moody algebras. We prove that these Kostka-Foulkes polynomials coincide with the… (More)

- Sankaran Viswanath
- Electr. J. Comb.
- 2006

We give an elementary combinatorial proof of a special case of a result due to Bazlov and Ion concerning the Fourier coefficients of the Cherednik kernel. This can be used to give yet another proof… (More)

We show that the rank 10 hyperbolic Kac–Moody algebra E10 contains every simply laced hyperbolic Kac–Moody algebra as a Lie subalgebra. Our method is based on an extension of earlier work of Feingold… (More)

We study the generating functions for Lusztig’s t-analog of weight multiplicities associated to integrable highest weight representations of the simplest affine Lie algebra $$A_1^{(1)}$$A1(1). These… (More)

We study generating functions for Lusztig's $t$-analog of weight multiplicities associated to integrable highest weight representations of the simplest affine Lie algebra $A_1^{(1)}$. At $t=1$, these… (More)

- K. N. Raghavan, B. Ravinder, Sankaran Viswanath
- J. Comb. Theory, Ser. A
- 2016

Abstract This paper is a study of the bases introduced by Chari–Loktev in [1] for local Weyl modules of the current algebra associated to a special linear Lie algebra. Partition overlaid patterns,… (More)

We study Lusztig's t-analog of weight multiplicities associated to level one representations of twisted affine Kac-Moody algebras. An explicit closed form expression is obtained for the corresponding… (More)