scholarly journals A quiver variety approach to root multiplicities

2021 ◽  
Vol 4 (1) ◽  
pp. 163-174
Author(s):  
Peter Tingley
Keyword(s):  
Quiver Variety ◽  
Root Multiplicities

ROOT MULTIPLICITIES OF THE INDEFINITE KAC-MOODY LIE ALGEBRAS AND

2002 ◽  
Vol 30 (6) ◽  
pp. 2941-2959 ◽  
Author(s):  
Jennifer Hontz ◽  
Kailash C. Misra
Keyword(s):  
Lie Algebras ◽  
Root Multiplicities

scholarly journals Normality of orbit closures in the enhanced nilpotent cone

2011 ◽  
Vol 203 ◽  
pp. 1-45 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson ◽  
Benjamin F. Jones
Keyword(s):  
Nilpotent Orbit ◽  
Complete Intersections ◽  
Quiver Variety ◽  
Quiver Varieties ◽  
Nilpotent Cone ◽  
Orbit Closures ◽  
Special Cases

AbstractWe continue the study of the closures of GL(V)-orbits in the enhanced nilpotent cone V × N begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.

scholarly journals On generalized category $$\mathcal {O}$$ for a quiver variety

2016 ◽  
Vol 368 (1-2) ◽  
pp. 483-536 ◽  
Author(s):  
Ben Webster
Keyword(s):  
Quiver Variety

scholarly journals ROOT MULTIPLICITIES AND NUMBER OF NONZERO COEFFICIENTS OF A POLYNOMIAL

2007 ◽  
Vol 06 (03) ◽  
pp. 469-475 ◽  
Author(s):  
SANDRO MATTAREI
Keyword(s):  
Finite Field ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Similar Argument ◽  
Original Result ◽  
Exact Number ◽  
Nonzero Root ◽  
Root Multiplicities ◽  
Univariate Polynomial

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.

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

1994 ◽  
Vol 170 (1) ◽  
pp. 277-299 ◽  
Author(s):  
S.J. Kang ◽  
D.J. Melville
Keyword(s):  
Root Multiplicities

Root multiplicities of extended-hyperbolic kac-moody algebras

1996 ◽  
Vol 24 (14) ◽  
pp. 4495-4512 ◽  
Author(s):  
N. Sthanumoorthy ◽  
A. Uma Maheswari
Keyword(s):  
Root Multiplicities

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

2008 ◽  
Vol 36 (2) ◽  
pp. 764-782 ◽  
Author(s):  
Vicky W. Klima ◽  
Kailash C. Misra
Keyword(s):  
Root Multiplicities
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