scholarly journals Generalized exponents of a free arrangement of hyperplanes and Shepherd-Todd-Brieskorn formula

1981 ◽  
Vol 63 (1) ◽  
pp. 159-179 ◽  
Author(s):  
Hiroaki Terao
Keyword(s):  
Arrangement Of Hyperplanes ◽  
Free Arrangement ◽  
Generalized Exponents

scholarly journals Generalized exponents of primitive two-colored digraphs

2009 ◽  
Vol 430 (5-6) ◽  
pp. 1550-1565 ◽  
Author(s):  
Yubin Gao ◽  
Yanling Shao
Keyword(s):  
Generalized Exponents

scholarly journals Depth in an Arrangement of Hyperplanes

1999 ◽  
Vol 22 (2) ◽  
pp. 167-176 ◽  
Author(s):  
P. J. Rousseeuw ◽  
M. Hubert
Keyword(s):  
Arrangement Of Hyperplanes

scholarly journals The deligne complex of a real arrangement of hyperplanes

1993 ◽  
Vol 131 ◽  
pp. 39-65 ◽  
Author(s):  
Luis Paris
Keyword(s):  
Vector Space ◽  
Finite Family ◽  
Real Vector Space ◽  
Real Vector ◽  
Arrangement Of Hyperplanes

Let V be a real vector space. An arrangement of hyperplanes in V is a finite family of hyperplanes of V through the origin. We say that is essential if ∩H ∊H = {0}

scholarly journals Combinatorics of Generalized Exponents

2018 ◽  
Vol 2020 (16) ◽  
pp. 4942-4992 ◽  
Author(s):  
Cédric Lecouvey ◽  
Cristian Lenart
Keyword(s):  
Root System ◽  
Lie Algebras ◽  
Finite Type ◽  
Irreducible Representations ◽  
Combinatorial Proof ◽  
Combinatorial Formula ◽  
Branching Rules ◽  
Crystal Graphs ◽  
Type C ◽  
Generalized Exponents

Abstract We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type $A_{n-1}$, we rederive the description of the generalized exponents in terms of crystal graphs without using the combinatorics of semistandard tableaux or the charge statistic. In finite type $C_{n}$, we obtain a combinatorial description of the generalized exponents based on the so-called distinguished vertices in crystals of type $A_{2n-1}$, which we also connect to symplectic King tableaux. This gives a combinatorial proof of the positivity of Lusztig $t$-analogs associated to zero-weight spaces in the irreducible representations of symplectic Lie algebras. We also present three applications of our combinatorial formula and discuss some implications to relating two type $C$ branching rules. Our methods are expected to extend to the orthogonal types.

scholarly journals Erratum to Free Arrangement and Rhombic Tilings

1997 ◽  
Vol 17 (3) ◽  
pp. 359-359
Author(s):  
P. H. Edelman ◽  
V. Reiner
Keyword(s):  
Free Arrangement
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