منابع مشابه
Paving Hessenberg Varieties by Affines
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety which arise in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent Hessenberg varieties for all classical types. This paving is in fact the intersection of a particular Bruhat decomposition with the Hes...
متن کاملHessenberg Varieties and Hyperplane Arrangements
Given a semisimple complex linear algebraic group G and a lower ideal I in positive roots of G, three objects arise: the ideal arrangement AI , the regular nilpotent Hessenberg variety Hess(N, I), and the regular semisimple Hessenberg variety Hess(S, I). We show that a certain graded ring derived from the logarithmic derivation module of AI is isomorphic to H∗(Hess(N, I)) and H∗(Hess(S, I)) , t...
متن کاملDecomposing Nilpotent Hessenberg Varieties over Classical Groups
Hessenberg varieties are a family of subvarieties of the flag variety, including the Springer fibers, the Peterson variety, and the entire flag variety itself. The seminal example arises from numerical analysis and consists, for a fixed linear operator M , of the full flags V1 ( V2 . . . ( Vn in GLn with MVi ⊆ Vi+1 for all i. In this paper, I show that all nilpotent Hessenberg varieties in type...
متن کاملFomenko–Mischenko Theory, Hessenberg Varieties, and Polarizations
The symmetric algebra S(g) over a Lie algebra g has the structure of a Poisson algebra. Assume g is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and A. Tarasev construct a polynomial subalgebra H = C[q1, . . . , qb] of S(g) which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of g. Let G be the adjoint group of g and let l = ...
متن کاملChromatic Quasisymmetric Functions and Hessenberg Varieties
We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian polynomials, the one in symmetric function theory deals with a refinement of the chromatic symmetric functions of Stanley, and the one in algebra...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2007
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-007-0038-4