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Categorification and supercategorification of highest weight modules over quantum generalized Kac-Moody algebras

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Authors
오세진
Advisor
강석진
Major
자연과학대학 수리과학부
Issue Date
2013-02
Publisher
서울대학교 대학원
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 강석진.
Abstract
Let $U_q(\g)$ be the quantum generalized Kac-Moody algebras and let $V(\Lambda)$ be the
integrable highest weight $U_q(\g)$-module. We prove that $V(\Lambda)$
can be categorified via the cyclotomic quiver Hecke algebra $\KLR^\Lambda$ and
supercategorified via the cyclotomic quiver Hecke superalgebras $\R^\Lambda$, simultaneously.
Moreover, since $U^-_q(\g)$ is the projective limit of
$V(\Lambda)$, $U^-_q(\g)$ can be also categorified via the quiver Hecke algebra $\KLR$ and
supercategorified via the quiver Hecke superalgebras $\R$, simultaneously.
Language
English
URI
https://hdl.handle.net/10371/121258
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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