Category O: gradings and translation functors

By C. Stroppel. 2003

113 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3a02f0a73605d30a0a32b0a374408f73148fecb9

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Citations in the corpus

Some homological properties of the category O (2007, methodology): “The necessary statement follows by tracking the grading, using [Stroppel 2003a; 2005].”
Category O and slk link invariants (2007, methodology): “Then in the Grothendieck group the shift functor will descend to the action of multiplication by the quantum parameter q. The theory of graded category O is due to W. Soergel and has been studied extensively by C. Stroppel [ Str1 ].”
A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products (2005, methodology): “t I˜(x·λ) be the injective hull of L˜(x·λ). Let d = HomC(•,C) denote a graded lift of the duality functor such that d(L) = Lfor any simple module Lconcentrated in degree zero (for properties see e.g. [Str03]). 3.4 Projective functors and the cohomology ring of the ﬂag variety The purpose of this sec”
Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors (2005, background): “Since all the occurring functors can be lifted to a Z-graded version (as explained in [ St ]), the natural transformations corresponding to cobordisms can be interpreted as (homogeneous) transformations between Z-functors.”
Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “(Strictly speaking, the arguments in [78] about the existence of graded lifts are only formulated for the principal block, but generalize directly to arbitrary integral blocks in the obvious way by taking invariants of the coinvariants.”
Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012, methodology): “Using the graded versions of translation functors as in [59], the proposition follows at least up to an overall shift.”
Quiver Schur algebras and q-Fock space (2011, background): “o handle in practice. (A similar phenomenon appears for the classical category Ofor semi-simple complex Lie algebras, where the Jantzen ﬁltration can also be described in terms of a grading, [BGS96], [Str03]. This grading is actually directly connected with the grading on the algebras Rν ∼=Hν in cas”
Projective-injective modules, Serre functors and symmetric algebras (2005, background): “On the other hand, ~ yiðLÞ is concentrated in the degrees 1, 0, 1 for any simple module L, concentrated in degree 0 ([60], Theorem 5.”
A combinatorial approach to functorial quantum slk knot invariants (2007, methodology): “12], [27]) Let F ∈ P(λ, ν) be indecomposable.”
Lectures on algebraic categorification (2010, background): “e functor Cλ⊗Cµ − is an exact endofunctor of Cλ-gmod. Since every indecomposable projective in Oλ is a direct summand of some module of the form θs 1θs 2 ···θs k P(λ), by standard arguments (see e.g. [St1]) we obtain that every VP(w· λ), w∈ W, can be considered as an object in Cλ-gmod (unique up to ”
Categorification of (induced) cell modules and the rough structure of generalized Verma modules (2007, unknown): “graded cases of (i) are treated in [BG, Theorem 3.4(iv)] and [ St2 , Theorem 7.1].”