Twisting functors on

By H. Andersen, C. Stroppel. 2003

58 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ce3447a68d5cf98b31bd0892f2d3ddb39a42f0e8

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In Algebra and Number Theory

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In Mathematical Physics

Citations in the corpus

On functors associated to a simple root (2004, methodology): “Proof. Let S be a short exact sequence of modules having a dual Verma flag; then G(S) is exact ([ AS , Theorem 2.2]) and hence Q(S) is right exact.”
Lectures on algebraic categorification (2010, methodology): “ition 6.5 it follows that Twdoes not depend (up to isomorphism) on the choice of the reduced decomposition. In the following claim we collected some combinatorial properties of twisting functors (see [AS]): Proposition 6.6. (a) For any µ∈ h∗ and any s∈ Swe have Ts∇(µ) = ( ∇(s· µ), µ<s· µ; ∇(µ), o”
Projective-injective modules, Serre functors and symmetric algebras (2005, background): “Now (5.2) follows from the Kazhdan-Lusztig conjectures, see [ AS03 , Theorem 6.3 and Theorem 7.8] for details.”
A combinatorial approach to functorial quantum slk knot invariants (2007, background): “Let T be the graded lift of the twisting functor ([1], [9, Section 5]) corresponding to the longest element w0 of the Weyl group such that T∆(x·λ) is mapped to d∆(w0x·λ).”
Endomorphisms of cell 2-representations (2012, unknown): “, equivalence of cell 2-representations corresponding to the same two-sided cell was obtained using Arkhipov’s twisting functors and the fact that they naturally commute with projective functors, see [AS]. Our present result shows that the shadows of Arkhipov’s twisting functors act, on a cell 2-rep”
Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “λ)] of the standard graded lift of the parabolic Verma module Mqk(λ) to vλ with head concentrated in degree zero. (The multiplication with q corresponds to the grading shift ⟨1⟩). Recall from [AL03], [AS03] the right exact twisting endofunctors Ti ∶= Tsα i of the integral category O attached to sαi.”
Categorification of (induced) cell modules and the rough structure of generalized Verma modules (2007, unknown): “graded cases of (ii) follow from [ AS , (2.3) and Theorem 3.2] and [MO2, Appendix].”
Some homological properties of the category O (2007, methodology): “Verma modules in Aigmod and LC(T) correspond via K by [MO2, Theorem 9]. Verma modules are acyclic for twisting functors by [ AS , Theorem 2.2] and for shuing functors by [MS2, Proposition 5.3].”