Another realization of the category of modules over the small quantum group

Arkhipov, Sergey; Gaitsgory, Dennis

doi:10.1016/s0001-8708(02)00016-6

Cited by 50 publications

(120 citation statements)

References 15 publications

Supporting

Mentioning

119

Contrasting

Order By: Relevance

“…Using these equivalences, it has been shown in [AG03] that the category D.Gr G / Hecke -mod I 0 , defined as above, is equivalent to the regular block u q .g/ -mod 0 of the category of modules over the small quantum group u q .g/. The tensor product by the line bundle ᏸ h _ can defines an equivalence D.Gr G / Hecke -mod…”

Section: T//=goeoetmentioning

confidence: 99%

See 1 more Smart Citation

Localization of g-modules on the affine Grassmannian

Frenkel

Gaitsgory

2009

Ann. Math.

Self Cite

View full text Add to dashboard Cite

We consider the category of modules over the affine Kac-Moody algebra b g of critical level with regular central character. In our previous paper we conjectured that this category is equivalent to the category of Hecke eigen-D-modules on the affine Grassmannian G..t //=GOEOEt . This conjecture was motivated by our proposal for a local geometric Langlands correspondence. In this paper we prove this conjecture for the corresponding I 0 equivariant categories, where I 0 is the radical of the Iwahori subgroup of G..t //. Our result may be viewed as an affine analogue of the equivalence of categories of g-modules and D-modules on the flag variety G=B, due to Beilinson-Bernstein and Brylinski-Kashiwara.

show abstract

Section: T//=goeoetmentioning

confidence: 99%

“…Then, according to [AG03] This conjecture has a number of interesting corollaries pertaining to the structure of the category of representations at the critical level:…”

Section: T//=goeoetmentioning

confidence: 99%

Localization of g-modules on the affine Grassmannian

Frenkel

Gaitsgory

2009

Ann. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…We start this subsection by recalling the definition of equivariantization of a fusion category. This notion has been considered by different authors, see [3,7,23,28]. We first present the construction for group actions on a linear category C, that is, dropping the tensor structure in C.…”

Section: 2mentioning

confidence: 99%

Hopf Algebra Extensions of Group Algebras and Tambara-Yamagami Categories

Natale

2009

Algebr Represent Theor

View full text Add to dashboard Cite

Abstract. We determine the structure of Hopf algebras that admit an extension of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called Tambara-Yamagami fusion categories. As a byproduct, we show that every semisimple Hopf algebra of dimension < 36 is necessarily group-theoretical; thus 36 is the smallest possible dimension where a non group-theoretical example occurs.

show abstract

“…Therefore, they obtain an equivalence between the category Q M and the deequivariantization of A M by G, see [ArG,Thm. 2.8].…”

Section: Proposition 31 Let H Be a Hopf Algebra And K ⊂ H A Cleft Cmentioning

confidence: 99%