2,511 research outputs found
Koszul gradings on Brauer algebras
We show that the Brauer algebra over the complex numbers for an integral
parameter delta can be equipped with a grading, in the case of delta being
non-zero turning it into a graded quasi-hereditary algebra. In which case it is
Morita equivalent to a Koszul algebra. This is done by realizing the Brauer
algebra as an idempotent truncation of a certain level two VW-algebra for some
large positive integral parameter N. The parameter delta appears then in the
choice of a cyclotomic quotient. This cyclotomic VW-algebra arises naturally as
an endomorphism algebra of a certain projective module in parabolic category O
for an even special orthogonal Lie algebra. In particular, the graded
decomposition numbers are given by the associated parabolic Kazhdan-Lusztig
polynomials.Comment: 28 page
Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra
We give a proof of a Schur-Weyl duality statement between the Brauer algebra
and the ortho-symplectic Lie superalgebra .Comment: 22 pages, minor changes, to appear in M
Relative cellular algebras
In this paper we generalize cellular algebras by allowing different partial
orderings relative to fixed idempotents. For these relative cellular algebras
we classify and construct simple modules, and we obtain other characterizations
in analogy to cellular algebras.
We also give several examples of algebras that are relative cellular, but not
cellular. Most prominently, the restricted enveloping algebra and the small
quantum group for , and an annular version of arc algebras.Comment: 39 pages, many figures, revised version, to appear in Transform.
Groups, comments welcom
Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)
We describe diagrammatically a positively graded Koszul algebra \mathbb{D}_k
such that the category of finite dimensional \mathbb{D}_k-modules is equivalent
to the category of perverse sheaves on the isotropic Grassmannian of type D_k
constructible with respect to the Schubert stratification. The connection is
given by an explicit isomorphism to the endomorphism algebra of a projective
generator described in by Braden. The algebra is obtained by a "folding"
procedure from the generalized Khovanov arc algebras. We relate this algebra to
the category of finite dimensional representations of the orthosymplectic
supergroups. The proposed equivalence of categories gives a concrete
description of the categories of finite dimensional SOSP(m|2n)-modules
Functoriality of colored link homologies
We prove that the bigraded colored Khovanov-Rozansky type A link and tangle
invariants are functorial with respect to link and tangle cobordisms.Comment: 41 pages, many colored figures, some changes following suggestions of
a referee, to appear in Proc. Lond. Math. Soc., comments welcom
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