Polyhedral realization of the highest weight crystals for generalized Kac-Moody algebras
نویسندگان
چکیده
منابع مشابه
Polyhedral Realization of the Highest Weight Crystals for Generalized Kac-moody Algebras
In this paper, we give a polyhedral realization of the highest weight crystals B(λ) associated with the highest weight modules V (λ) for the generalized Kac-Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac-Moody algebras of ranks 2, 3, and Monster algebras.
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In this paper, we give polyhedral realization of the crystal B(∞) of U− q (g) for the generalized Kac-Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac-Moody algebras of rank 2, 3 and Monster Lie algebras. Introduction In his study of Conway and Norton’s Moonshine Conjecture [3] for the infinite dimensional Z-graded representation V ♮ of the Mons...
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We present a geometric construction of highest weight crystals B(λ) for quantum generalized Kac-Moody algebras. It is given in terms of the irreducible components of certain Lagrangian subvarieties of Nakajima’s quiver varieties associated to quivers with edge loops. Introduction The 1990’s saw a great deal of interesting interplay between the geometry of quiver varieties and the representation...
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In this paper, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem and give a characterization of the crystals B(∞) and B(λ). Introduction The purpose of this paper is to develop the theory of abstract crystals for quantum generalized Kac-Moody algebras. In [6], the third auth...
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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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04446-2