4,773 research outputs found
Quasi-Coxeter categories and a relative Etingof-Kazhdan quantization functor
Let g be a symmetrizable Kac-Moody algebra and U_h(g) its quantized
enveloping algebra. The quantum Weyl group operators of U_h(g) and the
universal R-matrices of its Levi subalgebras endow U_h(g) with a natural
quasi-Coxeter quasitriangular quasibialgebra structure which underlies the
action of the braid group of g and Artin's braid groups on the tensor product
of integrable, category O modules. We show that this structure can be
transferred to the universal enveloping algebra Ug[[h]]. The proof relies on a
modification of the Etingof-Kazhdan quantization functor, and yields an
isomorphism between (appropriate completions of) U_h(g) and Ug[[h]] preserving
a given chain of Levi subalgebras. We carry it out in the more general context
of chains of Manin triples, and obtain in particular a relative version of the
Etingof-Kazhdan functor with input a split pair of Lie bialgebras. Along the
way, we develop the notion of quasi-Coxeter categories, which are to
generalized braid groups what braided tensor categories are to Artin's braid
groups. This leads to their succint description as a 2-functor from a
2-category whose morphisms are De Concini-Procesi associahedra. These results
will be used in the sequel to this paper to give a monodromic description of
the quantum Weyl group operators of an affine Kac-Moody algebra, extending the
one obtained by the second author for a semisimple Lie algebra.Comment: 63 pages. Exposition in sections 1 and 4 improved. Material added:
definition of a split pair of Lie bialgebras (sect. 5.2-5.5), 1-jet of the
relative twist (5.20), PROP description of the Verma modules L_-,N*_+ (7.6),
restriction to Levi subalgebras (8.4), D-structures on Kac-Moody algebras
(9.1
Algebraic K-theory of quasi-smooth blow-ups and cdh descent
We construct a semi-orthogonal decomposition on the category of perfect
complexes on the blow-up of a derived Artin stack in a quasi-smooth centre.
This gives a generalization of Thomason's blow-up formula in algebraic K-theory
to derived stacks. We also provide a new criterion for descent in Voevodsky's
cdh topology, which we use to give a direct proof of Cisinski's theorem that
Weibel's homotopy invariant K-theory satisfies cdh descent.Comment: 24 pages; to appear in Annales Henri Lebesgu
New Duality Transformations in Orbifold Theory
We find new duality transformations which allow us to construct the stress
tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the
set of all current-algebraic conformal field theories with a finite symmetry
group H \subset Aut(g). The permutation orbifolds with H = Z_\lambda and H =
S_3 are worked out in full as illustrations but the general formalism includes
both simple and semisimple g. The motivation for this development is the
recently-discovered orbifold Virasoro master equation, whose solutions are
identified by the duality transformations as sectors of the permutation
orbifolds A(D_\lambda)/Z_\lambda.Comment: 48 pages,typos correcte
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