Affine and degenerate affine BMW algebras: the center

@article{Daugherty2011AffineAD,
  title={Affine and degenerate affine BMW algebras: the center},
  author={Zajj Daugherty and Arun Ram and Rahbar Virk},
  journal={Osaka Journal of Mathematics},
  year={2011},
  volume={51},
  pages={257-283}
}
The degenerate affine and affine BMW algebras arise naturally in the co ntext of SchurWeyl duality for orthogonal and symplectic Lie algebras and quantum groups, respectively. Cyclotomic BMW algebras, affine Hecke algebras, cyclotomic Hecke algebras, and their degenerate versions are quotients. In this paper the theory is unified by treating the orthogonal and symplectic cases simultaneously; we make an exact parallel between the degenerate affine and affine cases via a new algebra which takes… 
Affine and degenerate affine BMW algebras: actions on tensor space
The affine and degenerate affine Birman–Murakami–Wenzl (BMW) algebras arise naturally in the context of Schur–Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively.
The degenerate affine walled Brauer algebra
We realize (via an explicit isomorphism) the walled Brauer algebra for an arbitrary integral parameter δ as an idempotent truncation of a level two cyclotomic degenerate affine walled Brauer algebra.
Degenerate two-boundary centralizer algebras
Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space.
The degenerate affine walled Brauer algebra
Abstract We define a degenerate affine version of the walled Brauer algebra, that has the same role played by the degenerate affine Hecke algebra for the symmetric group algebra. We use it to prove a
Characteristic maps for the Brauer algebra
The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them
Walled Brauer algebras as idempotent truncations of level 2 cyclotomic quotients
We realize (via an explicit isomorphism) the walled Brauer algebra for an arbitrary integral parameter delta as an idempotent truncation of a level two cyclotomic degenerate affine walled Brauer
K-theoretic analogues of factorial Schur P- and Q-functions
Abstract We introduce two families of symmetric functions generalizing the factorial Schur P - and Q -functions due to Ivanov. We call them K -theoretic analogues of factorial Schur P - and Q
TANGLE CATEGORIES AND SCHUR-WEYL DUALITY FOR CERTAIN INFINITE DIMENSIONAL Uqpsl2q-MODULES
We identify the type B Temperley-Lieb category TLBpq,Qq of marked diagrams as a subquotient of the coloured framed tangle category studied by Freyd, Yetter, Reshitikhin, Turaev and others, and use
Defining an Affine Partition Algebra
We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we
Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality
We describe how certain cyclotomic Nazarov-Wenzl algebras occur as endomorphism rings of projective modules in a parabolic version of BGG category O of type $D$. Furthermore we study a family of
...
1
2
3
...

References

SHOWING 1-10 OF 69 REFERENCES
Affine and degenerate affine BMW algebras: actions on tensor space
The affine and degenerate affine Birman–Murakami–Wenzl (BMW) algebras arise naturally in the context of Schur–Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively.
Affine braids, Markov traces and the category O
This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi
Affine Birman–Wenzl–Murakami algebras and tangles in the solid torus
The ordinary (or classical) Birman-Wenzl-Murakami algebras were initially conceived as an algebraic framework for the Kauffman link invariant. They also appear as centralizer algebras for
Affine Hecke algebras and generalized standard Young tableaux
Abstract This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite-dimensional irreducible calibrated representations. The primary technique
On the center of quantized enveloping algebras
Let U be a quasitriangular Hopf algebra. One may use the R-matrix of U in order to construct scalar invariants of knots. Analogously, Reshetikhin wrote tangle invariants which take their values in
On the freeness of the cyclotomic BMW algebras: admissibility and an isomorphism with the cyclotomic Kauffman tangle algebras
The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B k n , introduced by R. Haring- Oldenburg, are a generalisation of the BMW algebras associated with the cyclotomic Hecke algebras of type
Representations of graded Hecke algebras
Representations of affine and graded Hecke algebras associated to Weyl groups play an important role in the Langlands correspondence for the admissible representations of a reductive p-adic group. We
On the structure of cyclotomic Nazarov–Wenzl algebras
Ariki, Mathas and Rui [S. Ariki, A. Mathas, H. Rui, Cyclotomic Nazarov�Wenzl algebras, Nagoya Math. J. 182 (2006) 47�134 (special volume in honor of Professor G. Lusztig)] introduced a class of
Cyclotomic Nazarov-Wenzl Algebras
Abstract Nazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain “cyclotomic
Lie algebras and degenerate Affine Hecke Algebras of type A
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke
...
1
2
3
4
5
...