Path realization of crystal B(∞)

Document Type

Article

Publication Date

8-1-2011

Abstract

A class of piecewise linear paths, as a generalization of Littelmann's paths, are introduced, and some operators, acting on the above paths with fixed parametrization, are defined. These operators induce the ordinary Littelmann's root operators' action on the equi-alence classes of paths. With these induced operators, an explicit realization of B(∞) is given in terms of equivalence classes of paths, where B(∞) is the crystal base of the negative part of a quantum group Uq(g). Furthermore, we conjecture that there is a complete set of representatives for the above model by fixing a parametrization, and we prove the case when g is of finite type. © 2011 Higher Education Press and Springer-Verlag Berlin Heidelberg.

Publication Source (Journal or Book title)

Frontiers of Mathematics in China

First Page

689

Last Page

706

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