Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules
نویسندگان
چکیده
منابع مشابه
Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules
Since Kashiwara introduced the theory of crystal base ([2]) in 1990, one of the most fundamental problems has been to describe the crystal base associated with the given integrable highest weight module as explicitly as possible. In order to answer this, many kinds of new combinatorial objects have been invented, e.g., in [9] some analogues of Young tableaux were introduced in order to describe...
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Since pioneering works of G.Lusztig and M.Kashiwara on special bases for quantum groups, a lot of work has been done on the combinatorial structure of these bases. Although Lusztig’s canonical bases and Kashiwara’s global crystal bases were shown by Lusztig to coincide whenever both are defined, their constructions are quite different and lead to different combinatorial parametrizations. In thi...
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In [5],[6], Kashiwara introduced the theory of crystal base. He has shown that the existence of crystal base for the subalgebra U q (g) of the given quantum algebra Uq(g) and arbitrary integrable highest weight Uq(g)-modules. It is a fundamental problem to present a concerete realization of crystal bases for given integrable highest weight modules as explicitly as possible. Up to the present ti...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7920