TY - JOUR
AU - Halverson, T
AU - Mazzocco, M
AU - Ram, A
Y2 - 2014/05/21
Y1 - 2009/09/01
SN - 0027-7630
UR - http://hdl.handle.net/11343/29241
AB - AbstractWe 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.
LA - English
PB - NAGOYA UNIV
KW - Pure Mathematics
T1 - COMMUTING FAMILIES IN HECKE AND TEMPERLEY-LIEB ALGEBRAS
DO - 10.1017/S0027763000009740
IS - NAGOYA MATHEMATICAL JOURNAL
VL - 195
SP - 125-152
L1 - /bitstream/handle/11343/29241/277949_135000.pdf?sequence=1&isAllowed=n
ER -