Root multiplicities of some classes of extended-hyperbolic Kac-Moody and extended-hyperbolic generalized Kac-Moody algebras

It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial over a field of characteristic zero is larger than the multiplicity of any of its nonzero roots. We extend this result to an appropriate statement in positive characteristic. Furthermore, we present a new proof of the original result, which produces also the exact number of monic polynomials of a given degree for which the bound is attained. A similar argument allows us to determine the number of monic polynomials of a given degree, multiplicity of a given nonzero root, and number of nonzero coefficients, over a finite field of characteristic larger than the degree.

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Root Multiplicities of the Kac-Moody Algebras HA(1)n

Journal of Algebra ◽

10.1006/jabr.1994.1338 ◽

1994 ◽

Vol 170 (1) ◽

pp. 277-299 ◽

Cited By ~ 12

Author(s):

S.J. Kang ◽

D.J. Melville

Keyword(s):

Root Multiplicities

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Root multiplicities of extended-hyperbolic kac-moody algebras

Communications in Algebra ◽

10.1080/00927879608825828 ◽

1996 ◽

Vol 24 (14) ◽

pp. 4495-4512 ◽

Cited By ~ 7

Author(s):

N. Sthanumoorthy ◽

A. Uma Maheswari

Keyword(s):

Root Multiplicities

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Root Multiplicities of the Indefinite Kac–Moody Algebras of Symplectic Type

Communications in Algebra ◽

10.1080/00927870701724367 ◽

2008 ◽

Vol 36 (2) ◽

pp. 764-782 ◽

Cited By ~ 3

Author(s):

Vicky W. Klima ◽

Kailash C. Misra

Keyword(s):

Root Multiplicities

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ON ROOT MULTIPLICITIES OF $H A_n^{(1)}$

International Journal of Algebra and Computation ◽

10.1142/s0218196702000730 ◽

2002 ◽

Vol 12 (03) ◽

pp. 477-508 ◽

Cited By ~ 5

Author(s):

JENNIFER HONTZ ◽

KAILASH C. MISRA

Keyword(s):

Lie Algebra ◽

Irreducible Representations ◽

Root Multiplicities ◽

Multiplicity Formula

We determine the root multiplicities of the Kac–Moody Lie algebra [Formula: see text] of indefinite type using a recursive root multiplicity formula due to Kang. We view [Formula: see text] as a representation of its subalgebra [Formula: see text] and then use the combinatorics of the irreducible representations of [Formula: see text] to determine the root multiplicities.

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