منابع مشابه
Duality for nonlinear simply laced groups
We establish a character multiplicity duality for a certain natural class of nonlinear (nonalgebraic) groups arising as two-fold covers of simply laced real reductive algebraic groups. This allows us to extend part of the formalism of the Local Langlands Conjecture to such groups.
متن کاملBmw Algebras of Simply Laced Type
It is known that the recently discovered representations of the Artin groups of type An, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type Dn and En which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I1 and I2 with I...
متن کاملBrauer Algebras of Simply Laced Type
The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph An−1 on n− 1 nodes. Here we describe an algebra depending on an arbitrary graph M , called the Brauer algebra of type M , and study its structure in...
متن کاملLifting of Characters for Nonlinear Simply Laced Groups
One aspect of the Langlands program for linear groups is lifting of characters, which relates virtual representations on a group G with those on an endoscopic group for G. The goal of this paper is to extend this theory to nonlinear two-fold covers of real groups in the simply laced case. Suppose G̃ is a two-fold cover of a real reductive group G. The main result is that there is an operation, d...
متن کاملLevel-two Structure of Simply-laced Coxeter Groups
Let X be a graph, with corresponding simply-laced Coxeter group W . Then W acts naturally on the lattice L spanned by the vertices of X, preserving a quadratic form. We give conditions on X for the form to be nonsingular modulo two, and study the images of W −→ O(L/2kL). Introduction — This paper investigates the tower of 2-power congruence subgroups in a simply-laced Coxeter group, but the sto...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2017
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.08.009