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

Producción científica: Contribución a revista › Artículo de Investigación › revisión exhaustiva

1 Cita (Scopus)

Resumen

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).

Idioma original	Inglés estadounidense
Páginas (desde-hasta)	3-28
Número de páginas	26
Publicación	Journal of Algebra
Volumen	655
DOI	https://doi.org/10.1016/j.jalgebra.2023.09.007
Estado	Publicada - oct. 1 2024
Publicado de forma externa	Sí

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Álgebra y teoría de números

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10.1016/j.jalgebra.2023.09.007

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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).",

author = "Arias, \{Juan Camilo\} and Vyacheslav Futorny and Misra, \{Kailash C.\}",

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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

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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

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