Projective and Whittaker functors on category O

Juan Camilo Arias; Erik Backelin

doi:10.1016/j.jalgebra.2021.01.024

Projective and Whittaker functors on category O

Juan Camilo Arias, Erik Backelin

Research output: Contribution to journal › Research Article › peer-review

5 Scopus citations

Abstract

We show that the Whittaker functor on a regular block of the BGG-category O of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Miličić's equivalence between the category of Whittaker modules and a singular block of O. We show that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.

Original language	English (US)
Pages (from-to)	154-171
Number of pages	18
Journal	Journal of Algebra
Volume	574
DOIs	https://doi.org/10.1016/j.jalgebra.2021.01.024
State	Published - May 15 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2021.01.024

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title = "Projective and Whittaker functors on category O",

abstract = "We show that the Whittaker functor on a regular block of the BGG-category O of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Mili{\v c}i{\'c}'s equivalence between the category of Whittaker modules and a singular block of O. We show that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.",

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AU - Backelin, Erik

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N2 - We show that the Whittaker functor on a regular block of the BGG-category O of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Miličić's equivalence between the category of Whittaker modules and a singular block of O. We show that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.

AB - We show that the Whittaker functor on a regular block of the BGG-category O of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Miličić's equivalence between the category of Whittaker modules and a singular block of O. We show that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.

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UR - https://www.scopus.com/inward/citedby.url?scp=85100408362&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.01.024

DO - 10.1016/j.jalgebra.2021.01.024

M3 - Research Article

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VL - 574

SP - 154

EP - 171

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Projective and Whittaker functors on category O

Abstract

All Science Journal Classification (ASJC) codes

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