Duality between sln(C) and the Degenerate Affine Hecke Algebra

Tomoyuki Arakawa; Takeshi Suzuki

doi:10.1006/jabr.1998.7530

Duality between sl_n(C) and the Degenerate Affine Hecke Algebra

Tomoyuki Arakawa, Takeshi Suzuki

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

45 Citations (Scopus)

Abstract

We construct a family of exact functors from the Bernstein-Gelfand-Gelfand category O of sl_n-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebraH_lofGL_l. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simpleH_l-module can be thus obtained.

Original language	English
Pages (from-to)	288-304
Number of pages	17
Journal	Journal of Algebra
Volume	209
Issue number	1
DOIs	https://doi.org/10.1006/jabr.1998.7530
Publication status	Published - Nov 1 1998
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1006/jabr.1998.7530

Fingerprint Dive into the research topics of 'Duality between sl<sub>n</sub>(C) and the Degenerate Affine Hecke Algebra'. Together they form a unique fingerprint.

Cite this

@article{ed4ae9e9a7d2402c96d7c5fdc77e65a4,

title = "Duality between sln(C) and the Degenerate Affine Hecke Algebra",

abstract = "We construct a family of exact functors from the Bernstein-Gelfand-Gelfand category O of sln-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebraHlofGLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simpleHl-module can be thus obtained.",

author = "Tomoyuki Arakawa and Takeshi Suzuki",

note = "Funding Information: * Supported by JSPS, the Research Fellowships for Young Scientists.",

year = "1998",

month = nov,

day = "1",

doi = "10.1006/jabr.1998.7530",

language = "English",

volume = "209",

pages = "288--304",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Duality between sln(C) and the Degenerate Affine Hecke Algebra

AU - Arakawa, Tomoyuki

AU - Suzuki, Takeshi

N1 - Funding Information: * Supported by JSPS, the Research Fellowships for Young Scientists.

PY - 1998/11/1

Y1 - 1998/11/1

N2 - We construct a family of exact functors from the Bernstein-Gelfand-Gelfand category O of sln-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebraHlofGLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simpleHl-module can be thus obtained.

AB - We construct a family of exact functors from the Bernstein-Gelfand-Gelfand category O of sln-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebraHlofGLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simpleHl-module can be thus obtained.

UR - http://www.scopus.com/inward/record.url?scp=0009088099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009088099&partnerID=8YFLogxK

U2 - 10.1006/jabr.1998.7530

DO - 10.1006/jabr.1998.7530

M3 - Article

AN - SCOPUS:0009088099

VL - 209

SP - 288

EP - 304

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -