Cyclotomic Nazarov-Wenzl Algebras

By S. Ariki, Andrew Mathas, Hebing Rui. Nagoya mathematical journal, 2005

119 citations recorded by the source corpus.

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 quotients” of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank rn (2n−1)!! (when Ω is u-admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov-Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Wenzl algebra.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/45f8d7675d257751024728ac879965d8b44873e5

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Citations in the corpus

Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A (2009, background): “R T ] 1 5 Fe b This paper constructs an explicit homogeneous cellular basis for the cyclotomic Khovanov– Lauda–Rouquier algebras of type A. Keywords: Cyclotomic Hecke algebras, Khovanov–Lauda–Rouquier algebras, cellular algebras 2000 MSC: 20C08, 20C30”
Schur–Weyl duality for higher levels (2006, methodology): “We point out finally by [ AMR , Theorem 6.11] that Hd(, c), hence also the higher level Schur algebra Wd(, c), is a semisimple algebra if and only if d qi qj for all 1 i < j l with ci = cj.”
Graded Specht modules (2009, methodology): “The proofs in the degenerate case are entirely analogous to the proofs in the non-degenerate case, using the main result of [7] together with [5], §6, for the required construction of standard bases of Specht modules in that setting.”
Graded decomposition numbers for cyclotomic Hecke algebras (2009, methodology): “ordered by �. For the explicit construction of the underlying cell datum, we refer the reader to [DJM]; see also [ AMR , §6] for the appropriate modifications in the degenerate case.”
Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “Based on [6] we introduce a labelling set for a basis in the cyclotomic quotients and connect it with the counting of Verma modules from Proposition 2.”
Categorifications and cyclotomic rational double affine Hecke algebras (2013, unknown): “the notation, we assume that [−m, n] = [1, 2].”
Seminormal forms and Gram determinants for cellular algebras (2006, background): “It should be possible to find JM-elements for other cellular algebras such as the partition algebras and the cyclotomic Nazarov-Wenzl algebras [2].”