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Some branching formulas for Kac--Moody Lie algebras
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In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $T$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in \cite{JWm18}. We also make some conjectures about the generic rings.
Abstract
In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $T$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in \cite{JWm18}. We also make some conjectures about the generic rings.
참고문헌 (7)
- L. W. Christensen, "On the structure of almost complete intersections of codimension 3, in preparation", ~
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- J. Hong, "Introduction to Quantum Groups and Crystal bases", Gradu-ate Studies in Mathematics, 42 (2002), American Mathematical Society[DOI]
- M. Kashiwara, "On crystal bases of the Q-analogue of universal enveloping algebras", Duke Mathematical Journal, 63(2), pp.465~516 (1991), Duke University Press[DOI]
- S. Kumar, "Their Flag Varieties and Representation Theory", Progress in Mathematics, 204, pp.1007~ (2002), Birkhauser Boston, Inc[DOI]
- "The Sage Mathematics Software System (Version 8.0)" (2017)[URL]
- J. Weyman, "Generic free resolutions and root systems", Ann. Inst. Fourier (Grenoble), 68(3), pp.1241~1296 (2018)[DOI]
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