Combinatorics, symmetric functions, and Hilbert schemes
By Mark D. Haiman. 2002
179 citations recorded by the source corpus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/de286390c7816c8d7c191882e5a392d522f63242
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Higher Trivariate Diagonal Harmonics via generalized Tamari Posets (2011, background): “mension n!, and isomorphic to the regular representation of S n, for the action that permutes variables. The description of the case of two sets of variables took close to 15 years to be nalized (see [17]), and much remains to be understood. It is of dimension (n+ 1)n 1. It has been observed by Haim”
- Refined knot invariants and Hilbert schemes (2013, unknown): “the vector space K. This basis is orthogonal with respect to the pairing (29): (Iλ,Iµ) = δλ,µ ·gλ where: (31) gλ := Λ•(T∨ λ Hilbd) = Y ∈λ (1− qa( )t −l( ) 1) Y ∈λ (1− q −a ( )1tl ) Theorem 4.2. (e.g. [38, 48]) Under the isomorphism K ∼= V of Theorem 4.1, the classes Iλ ∈ K correspond to the renormal”
- Affine Springer fibers of type A and combinatorics of diagonal coinvariants (2012, background): “doubled analogue of Rn. This is related to q,t-analogue of Kostka-Foulkes polynomials or Macdonald polynomials. ∗thikita@math.kyoto-u.ac.jp 1 2 Let H˜ µ be the modified Macdonald polynomials (see e.g. [11] for the definition). The H˜ µ’s form a basis of the ring of symmetric polynomials with coefficient”
- Multivariate diagonal coinvariant spaces for complex reflection groups (2011, background): “alculations on symmetric 8 F.BERGERON functions2, we get Hn(w;t) = X λ⊢n n λ t mλ(w), (22) where n λ t := n!t λ 1!t ···λk!t , with n!t := (1+t)(1+t+t2)···(1+t+...+tn−1). In view of results in [9], we must also have that Hn(w;q,t) = ∇(en+1(w)) (23) where ∇ is an operator on symmetric functions, h”