School of Mathematics and Statistics - Research Publications

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Affine Braids, Markov traces and the category O

Orellana, ; RAM, A (American Mathematical Society, 2007)
COMMUTING FAMILIES IN HECKE AND TEMPERLEY-LIEB ALGEBRAS

Halverson, T ; Mazzocco, M ; Ram, A (NAGOYA UNIV, 2009-09)

Abstract We define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements in the affine Hecke algebra of type A, which in turn come from the Casimir element of the quantum group . We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.
Combinatorics in affine flag varieties

Parkinson, J ; Ram, A ; Schwer, C (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009-06-01)