Abstract
From the special linear Lie algebra An = st(n + 1,Q we construct certain indefinite Kac-Moody Lie algebras IAn(a, b) and then use the representation theory of An to determine explicit closed form root multiplicity formulas for the roots a of /An(α, b) whose degree satisfies \deg(a) < 2a + 1. These expressions involve the well-known Littlewood-Richardson coefficients and Kostka numbers. Using the Euler-Poincare Principle and Kostant's formula, we derive two expressions, one of which is recursive and the other closed form, for the multiplicity of an arbitrary root a of IAn(a, b) as a polynomial in Kostka numbers.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
