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arXiv · 1205.5245

Reading the dual Garside length of braids from homological and quantum representations

Tetsuya Ito
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Abstract

We show that Lawrence's representation and linear representations from quantum sl_2 called generic highest weight vectors detect the dual Garside length of braids in a simple and natural way. That is, by expressing a representation as a matrix over a Laurent polynomial ring using certain natural basis, the span of the variable is equal to the constant multiples of the dual Garside length.

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Tetsuya Ito. 2012-05-23. Reading the dual Garside length of braids from homological and quantum representations. https://arxiv.org/abs/1205.5245

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