Invariant subspaces of the LawrenceKrammer representation
Author:
Claire Levaillant
Journal:
Proc. Amer. Math. Soc. 140 (2012), 25992612
MSC (2010):
Primary 20F36; Secondary 20C08
Published electronically:
November 30, 2011
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Abstract: The LawrenceKrammer representation was used in to show the linearity of the braid group. The problem had remained open for many years. The fact that the LawrenceKrammer representation of the braid group is reducible for some complex values of its two parameters is now known, as well as the complete description of these values. It is also known that when the representation is reducible, the action on a proper invariant subspace is an IwahoriHecke algebra action. In this paper, we prove a theorem of classification for the invariant subspaces of the LawrenceKrammer space. We classify the invariant subspaces in terms of Specht modules. We fully describe them in terms of dimension and spanning vectors in the LawrenceKrammer space.
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 H.R. Morton and A.J. Wasserman, A basis for the BirmanWenzl algebra, preprint, 1989.
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Additional Information
Claire Levaillant
Affiliation:
Department of Mathematics, Caltech, Pasadena, California 91125
Address at time of publication:
Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106
Email:
cl@caltech.edu, claire@math.ucsb.edu
DOI:
http://dx.doi.org/10.1090/S000299392011111079
PII:
S 00029939(2011)111079
Keywords:
Braid groups,
representation theory
Received by editor(s):
July 31, 2010
Received by editor(s) in revised form:
January 28, 2011, February 15, 2011, and March 4, 2011
Published electronically:
November 30, 2011
Communicated by:
Birge HuisgenZimmermann
Article copyright:
© Copyright 2011
American Mathematical Society
