Young Tableaux and Crystal B(∞) for Finite Simple Lie Algebras
نویسندگان
چکیده
We study the crystal base of the negative part of a quantum group. An explicit realization of the crystal is given in terms of Young tableaux for types An, Bn, Cn, Dn, and G2. Connection between our realization and a previous realization of Cliff is also given.
منابع مشابه
Description of B(∞) through Kashiwara Embedding for E6 and E7 Lie Algebra Types
We study the crystal base B(∞) associated with the negative part of the quantum group for finite simple Lie algebras of types E6 and E7. We present an explicit description of B(∞) as the image of a Kashiwara embedding that is in natural correspondence with the tableau description of B(∞).
متن کاملYoung Tableaux, Nakajima Monomials, and Crystals for Special Linear Lie Algebras
Nakajima introduced a certain set of monomials characterizing the irreducible highest weight crystals B(λ). The monomial set can be extended so that it contains B(∞) in addition to B(λ). We give explicit new realizations of the crystals B(∞) and B(λ) over special linear Lie algebras in the language of extended Nakajima monomials. Also, we introduce Young tableau realization of the crystal B(∞) ...
متن کاملNakajima Monomials and Crystals for Special Linear Lie Algebras
The theory of Nakajima monomials is a combinatorial scheme for realizing crystal bases of quantum groups. Nakajima introduced a certain set of monomials realizing the irreducible highest weight crystals in [16]. Kashiwara and Nakajima independently defined a crystal structure on the set of Nakajima monomials and also gave a realization of irreducible highest weight crystal B(λ) in terms of Naka...
متن کاملCorrespondence between Young Walls and Young Tableaux Realizations of Crystal Bases for the Classical Lie Algebras
We give a 1-1 correspondence with the Young wall realization and the Young tableau realization of the crystal bases for the classical Lie algebras. Introduction Young tableaux and Young walls play important roles in the interplay, which can be explained in a beautiful manner using the crystal base theory for quantum groups, between the fields of representation theory and combinatorics. Indeed, ...
متن کاملCrystal Bases and Monomials for Uq(G2)-modules
In this paper, we give a new realization of crystal bases for irreducible highest weight modules over Uq(G2) in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization. Introduction In 1985, the quantum groups Uq(g), which may be thought of as q-deformations of the universal enveloping algebras U(g) of Kac-Moody algebras g, were introd...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008