Results 1  10
of
91
BMW algebras of simply laced type
 J. Algebra 286 (2005), 107–153. NAZAROV–WENZL ALGEBRAS 57
"... Abstract. 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 correspondi ..."
Abstract

Cited by 17 (7 self)
 Add to MetaCart
conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than An. 1.
BRAUER ALGEBRAS OF SIMPLY LACED TYPE
, 704
"... Abstract. The diagram algebra introduced by Brauer that describes the centralizer algebra of the nfold 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 a ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
an algebra depending on an arbitrary graph M, called the Brauer algebra of type M, and study its structure in the cases where M is a Coxeter graph of simply laced spherical type (so its connected components are of type An−1, Dn, E6, E7, E8). We determine the representations and find the dimension
A POSET CONNECTED TO ARTIN MONOIDS OF SIMPLY LACED TYPE
, 2005
"... Abstract. Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several Worbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order o ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Abstract. Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several Worbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order
LEFTCONNECTEDNESS OF SOME LEFT CELLS IN CERTAIN COXETER GROUPS OF SIMPLYLACED TYPE
"... Abstract. Let W be an irreducible finite or affine Weyl group of simplylaced type. We show that any w ∈ W with a(w) 6 6 satisfies Condition (C): w = x · wJ · y for some x, y ∈ W and some J ⊆ S with WJ finite and `(wJ) = a(w) (see 0.10.2 for the notation wJ, WJ, `(w) and a(w)). We also show that i ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. Let W be an irreducible finite or affine Weyl group of simplylaced type. We show that any w ∈ W with a(w) 6 6 satisfies Condition (C): w = x · wJ · y for some x, y ∈ W and some J ⊆ S with WJ finite and `(wJ) = a(w) (see 0.10.2 for the notation wJ, WJ, `(w) and a(w)). We also show
An approach to non simply laced cluster algebras
 Preprint arXiv:math.RT/0512043
, 2005
"... We study cluster algebras associated to a quiver equipped with a group of admissible automorphisms. This enables us to realize cluster algebras of non simply laced types as quotients of cluster algebras of simply laced types. We then generalize well known results on cluster algebras as denominators ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
We study cluster algebras associated to a quiver equipped with a group of admissible automorphisms. This enables us to realize cluster algebras of non simply laced types as quotients of cluster algebras of simply laced types. We then generalize well known results on cluster algebras as denominators
Cluster algebras and quantum affine algebras
, 2009
"... Let C be the category of finitedimensional representations of a quantum affine algebra Uq(̂g) of simplylaced type. We introduce certain monoidal subcategories Cℓ (ℓ ∈ N) of C ..."
Abstract

Cited by 71 (10 self)
 Add to MetaCart
Let C be the category of finitedimensional representations of a quantum affine algebra Uq(̂g) of simplylaced type. We introduce certain monoidal subcategories Cℓ (ℓ ∈ N) of C
SIMPLYLACED COXETER GROUPS AND GROUPS GENERATED BY SYMPLECTIC TRANSVECTIONS
, 1999
"... Let W be an arbitrary Coxeter group of simplylaced type (possibly infinite but of finite rank), let u and v be any two elements in W, and let i be a reduced word (of length m) for the pair (u, v) in the Coxeter group W × W. Generalizing a construction in [10, 11], we associate to i a subgroup Γi i ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
Let W be an arbitrary Coxeter group of simplylaced type (possibly infinite but of finite rank), let u and v be any two elements in W, and let i be a reduced word (of length m) for the pair (u, v) in the Coxeter group W × W. Generalizing a construction in [10, 11], we associate to i a subgroup Γi
STANDARD MODULES OF QUANTUM AFFINE ALGEBRAS
 DUKE MATHEMATICAL JOURNAL VOL. 111, NO. 3
, 2002
"... We give a proof of the cyclicity conjecture of Akasaka and Kashiwara for simply laced types, via quiver varieties. We also get an algebraic characterization of the standard modules. ..."
Abstract

Cited by 29 (2 self)
 Add to MetaCart
We give a proof of the cyclicity conjecture of Akasaka and Kashiwara for simply laced types, via quiver varieties. We also get an algebraic characterization of the standard modules.
The minimal degeneration singularities in the affine Grassmannians
 Duke Math. J
, 2005
"... Abstract. The minimal degeneration singularities in the affine Grassmannians of simple simplylaced algebraic groups are determined to be either Kleinian singularities of type A, or closures of minimal orbits in nilpotent cones. The singularities for nonsimplylaced types are studied by intersectio ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. The minimal degeneration singularities in the affine Grassmannians of simple simplylaced algebraic groups are determined to be either Kleinian singularities of type A, or closures of minimal orbits in nilpotent cones. The singularities for nonsimplylaced types are studied
Extended affine root systems IV (SimplyLaced Elliptic Lie Algebras
 Publ. RIMS, Kyoto Univ
"... Abstract.. Let (R,G) be a pair consisting of an elliptic root system R with a marking G. Assume that the attached elliptic Dynkin diagram Γ(R,G) is simplylaced (see Sect. 2). We associate three Lie algebras, explained in 1), 2) and 3) below, to the elliptic root system, and show that all three are ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
Abstract.. Let (R,G) be a pair consisting of an elliptic root system R with a marking G. Assume that the attached elliptic Dynkin diagram Γ(R,G) is simplylaced (see Sect. 2). We associate three Lie algebras, explained in 1), 2) and 3) below, to the elliptic root system, and show that all three
Results 1  10
of
91