Weyl Groups Associated with Affine Reflection Systems of Type $A_1$ (Coxeter Type Defining Relations)
نویسندگان
چکیده
منابع مشابه
Realization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
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Coloured generalised Young diagrams T (w) are introduced that are in bijective correspondence with the elements w of the Weyl-Coxeter group W of g, where g is any one of the classical affine Lie algebras g = A (1) ` , B (1) ` , C (1) ` , D (1) ` , A (2) 2` , A (2) 2`−1 or D (2) `+1. These diagrams are coloured by means of periodic coloured grids, one for each g, which enable T (w) to be constru...
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The Garnir relations play a very important role in giving combinatorial constructions of representations of the symmetric groups. For the Weyl groups of type Cn, having obtained the alternacy relation, we give an explicit combinatorial description of the Garnir relation associated with a ∆-tableau in terms of root systems. We then use these relations to find a K-basis for the Specht modules of ...
متن کاملrealization of locally extended affine lie algebras of type $a_1$
locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
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ژورنال
عنوان ژورنال: Publications of the Research Institute for Mathematical Sciences
سال: 2013
ISSN: 0034-5318
DOI: 10.4171/prims/99