Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras

Juan Camilo Arias; Vyacheslav Futorny; Kailash C. Misra

doi:10.1016/j.jalgebra.2023.09.007

Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras

Juan Camilo Arias
, Vyacheslav Futorny
, Kailash C. Misra

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

1 Scopus citations

Abstract

We consider reduced imaginary Verma modules for the untwisted quantum affine algebras U_q(gˆ) and define a crystal-like base which we call imaginary crystal base using the Kashiwara algebra K_q constructed in earlier work by Ben Cox and two of the authors. We prove the existence of the imaginary crystal base for any object in a suitable category O_red,im^q containing the reduced imaginary Verma modules for U_q(gˆ).

Original language	English (US)
Pages (from-to)	3-28
Number of pages	26
Journal	Journal of Algebra
Volume	655
DOIs	https://doi.org/10.1016/j.jalgebra.2023.09.007
State	Published - Oct 1 2024
Externally published	Yes

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This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 1 No Poverty

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2023.09.007

Cite this

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title = "Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras",

abstract = "We consider reduced imaginary Verma modules for the untwisted quantum affine algebras Uq(gˆ) and define a crystal-like base which we call imaginary crystal base using the Kashiwara algebra Kq constructed in earlier work by Ben Cox and two of the authors. We prove the existence of the imaginary crystal base for any object in a suitable category Ored,imq containing the reduced imaginary Verma modules for Uq(gˆ).",

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AU - Arias, Juan Camilo

AU - Futorny, Vyacheslav

AU - Misra, Kailash C.

PY - 2024/10/1

Y1 - 2024/10/1

N2 - We consider reduced imaginary Verma modules for the untwisted quantum affine algebras Uq(gˆ) and define a crystal-like base which we call imaginary crystal base using the Kashiwara algebra Kq constructed in earlier work by Ben Cox and two of the authors. We prove the existence of the imaginary crystal base for any object in a suitable category Ored,imq containing the reduced imaginary Verma modules for Uq(gˆ).

AB - We consider reduced imaginary Verma modules for the untwisted quantum affine algebras Uq(gˆ) and define a crystal-like base which we call imaginary crystal base using the Kashiwara algebra Kq constructed in earlier work by Ben Cox and two of the authors. We prove the existence of the imaginary crystal base for any object in a suitable category Ored,imq containing the reduced imaginary Verma modules for Uq(gˆ).

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UR - https://www.scopus.com/pages/publications/85172465625#tab=citedBy

U2 - 10.1016/j.jalgebra.2023.09.007

DO - 10.1016/j.jalgebra.2023.09.007

M3 - Research Article

AN - SCOPUS:85172465625

SN - 0021-8693

VL - 655

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EP - 28

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Crystal bases for reduced imaginary Verma modules of untwisted quantum affine algebras

Abstract

UN SDGs

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