# 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…

## 21 Citations

Affine and degenerate affine BMW algebras: actions on tensor space

- Mathematics
- 2012

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

- 2014

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

- Mathematics
- 2010

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

- Mathematics
- 2014

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

- Mathematics
- 2013

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

- Mathematics
- 2014

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

- Mathematics
- 2013

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

- 2019

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

- Mathematics
- 2021

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

- MathematicsAdvances in Mathematics
- 2018

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…

## References

SHOWING 1-10 OF 69 REFERENCES

Affine and degenerate affine BMW algebras: actions on tensor space

- Mathematics
- 2012

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

- Mathematics
- 2004

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

- Mathematics
- 2004

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

- Mathematics
- 2003

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

- 2005

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

- Mathematics
- 2009

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

- Mathematics
- 2002

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

- Mathematics
- 2008

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

- MathematicsNagoya Mathematical Journal
- 2006

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

- Mathematics
- 1997

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…