TY - JOUR

T1 - A topological approach to representations of the Iwahori-Hecke algebra

AU - Lawrence, RJ

PY - 1990/8/20

Y1 - 1990/8/20

N2 - In this paper a topological construction of representations of the -series of Hecke algebras, associated with 2-row Young diagrams, will be announced. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle over the configuration space of η points in the complex plane. The fibres are homology spaces of configuration spaces of points in a punctured complex plane, with a suitable twisted local coefficient system, and there is thus a natural flat connection on the vector bundle. It is also shown that there is a close correspondence between this construction and the work of Tsuchiya and Kanie, in which the monodromy of n-point functions for a conformal field theory on P1 is used to produce a braid group representation which factors through the Hecke algebra.

AB - In this paper a topological construction of representations of the -series of Hecke algebras, associated with 2-row Young diagrams, will be announced. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle over the configuration space of η points in the complex plane. The fibres are homology spaces of configuration spaces of points in a punctured complex plane, with a suitable twisted local coefficient system, and there is thus a natural flat connection on the vector bundle. It is also shown that there is a close correspondence between this construction and the work of Tsuchiya and Kanie, in which the monodromy of n-point functions for a conformal field theory on P1 is used to produce a braid group representation which factors through the Hecke algebra.

UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=starter5-25&SrcAuth=WosAPI&KeyUT=WOS:A1990DP80700007&DestLinkType=FullRecord&DestApp=WOS

U2 - 10.1142/S0217751X90002178

DO - 10.1142/S0217751X90002178

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

SN - 0217-751X

VL - 5

SP - 3213

EP - 3219

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 16

ER -