A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties

Mbirika, Aba

doi:10.48550/arxiv.0911.4962

Cited by 1 publication

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“…Next we give a basis OB(λ) for OH(X λ ) as a free abelian group. The monomials in this basis are the same as those for H(X λ ) first given by De Concini-Procesi [9] and further studied by Garsia-Procesi [16] and others [5,30,3]. Our description most closely resembles that of Mbirika For 1 ≤ i ≤ h(λ), define λ (i) to be the partition of n − 1 obtained from λ by doing the following.…”

Section: Odd Cohomologymentioning

confidence: 93%

“…The exponent of the variable x j is just the height minus one of the corresponding box in the tableau t. It is not difficult to check that this map is a bijection between the set of standard tableaux of shape λ and elements of maximal degree in OB(λ). This bijection is extended to a bijection between all row standard tableau and monomials of shape λ in [30].…”

Section: 2mentioning

confidence: 99%

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Oddification of the Cohomology of Type A Springer Varieties

Lauda

Russell

2013

International Mathematics Research Notices

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We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are 'odd' analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identified with the corresponding Specht module of the Hecke algebra at q = −1.

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