Macdonald polynomials and BGG reciprocity for current algebras

Matthew Bennett; Arkady Berenstein; Vyjayanthi Chari; Anton Khoroshkin; Sergey Loktev

doi:10.1007/s00029-013-0141-7

Macdonald polynomials and BGG reciprocity for current algebras

Matthew Bennett, Arkady Berenstein, Vyjayanthi Chari, Anton Khoroshkin, Sergey Loktev

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

Abstract

We study the category I_gr of graded representations with finite-dimensional graded pieces for the current algebra g⊗C[t] where g is a simple Lie algebra. This category has many similarities with the category O of modules for g, and in this paper, we prove an analog of the famous BGG duality in the case of sl_n+1.

Original language	American English
Pages (from-to)	585-607
Number of pages	23
Journal	Selecta Mathematica, New Series
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s00029-013-0141-7
State	Published - Apr 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Physics and Astronomy
General Mathematics

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10.1007/s00029-013-0141-7

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title = "Macdonald polynomials and BGG reciprocity for current algebras",

abstract = "We study the category Igr of graded representations with finite-dimensional graded pieces for the current algebra g⊗C[t] where g is a simple Lie algebra. This category has many similarities with the category O of modules for g, and in this paper, we prove an analog of the famous BGG duality in the case of sln+1.",

author = "Matthew Bennett and Arkady Berenstein and Vyjayanthi Chari and Anton Khoroshkin and Sergey Loktev",

note = "Funding Information: A.B. was partially supported by DMS-0800247 and DMS-1101507. V.C. was partially supported by DMS-0901253. S.L. was partially supported by RFBR-CNRS-11-01-93105 and RFBR-12-01-00944. A.K was supported by the grants NSh-3349.2012.2, RFBR-10-01-00836, RFBR-CNRS-10-01-93111, RFBR-CNRS-10-01-93113, and by the Simons Foundation.",

year = "2014",

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doi = "10.1007/s00029-013-0141-7",

language = "American English",

volume = "20",

pages = "585--607",

journal = "Selecta Mathematica, New Series",

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AU - Bennett, Matthew

AU - Berenstein, Arkady

AU - Chari, Vyjayanthi

AU - Khoroshkin, Anton

AU - Loktev, Sergey

N1 - Funding Information: A.B. was partially supported by DMS-0800247 and DMS-1101507. V.C. was partially supported by DMS-0901253. S.L. was partially supported by RFBR-CNRS-11-01-93105 and RFBR-12-01-00944. A.K was supported by the grants NSh-3349.2012.2, RFBR-10-01-00836, RFBR-CNRS-10-01-93111, RFBR-CNRS-10-01-93113, and by the Simons Foundation.

PY - 2014/4

Y1 - 2014/4

N2 - We study the category Igr of graded representations with finite-dimensional graded pieces for the current algebra g⊗C[t] where g is a simple Lie algebra. This category has many similarities with the category O of modules for g, and in this paper, we prove an analog of the famous BGG duality in the case of sln+1.

AB - We study the category Igr of graded representations with finite-dimensional graded pieces for the current algebra g⊗C[t] where g is a simple Lie algebra. This category has many similarities with the category O of modules for g, and in this paper, we prove an analog of the famous BGG duality in the case of sln+1.

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EP - 607

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 2

ER -

Macdonald polynomials and BGG reciprocity for current algebras

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