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Fermionic Diagonal Coinvariants / Jongwon Kim.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Kim, Jongwon, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Physical Description:
- 1 online resource (84 pages)
- Distribution:
- Ann Arbor : ProQuest Dissertations & Theses, 2022
- Contained In:
- Dissertations Abstracts International 84-01B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania, 2022.
- Language Note:
- English
- Summary:
- Let W be a complex reflection group of rank n acting on its reflection representation V ≅ Cn. The doubly graded action of W on the exterior algebra ∧(V ⊕ V*) induces an action on the quotient by the ideal generate by W-invariants with vanishing constant term FDRW = ∧ (V ⊕ V*) / ⟨ ∧ (V ⊕ V*)W_{+} ⟩. We describe the bi-graded W-module structure of FDRW and introduce a variant of Motzkin paths that descends to the standard monomial basis of FDRW with respect to certain term order. The top degree of FDRW exhibits the Narayana refinement of Catalan numbers. When W = Sn, the symmetric group, FDRSn ≅ Rn,0,2, where Rn,0,2 is the special case of the Boson-Fermionic diagonal coinvariants with two sets of Fermionic variables. In this case, the (i,j)-th degree component is a difference of Kronecker product of two hook Schur functions.In addition we consider a module Mn,m spanned by m-ary strings of length n. When m = 2, as a vector space, Mn,2 ≅ C[Xn] / ⟨ x12, ... , xn2 ⟩. The trivial component of drn ⊗ Mn,2 is a weighted sum of q,t-Narayana numbers which is a different q,t-Catalan number than the alternant of drn. At t = 1, the trivial component equals the inversion generating function for 321-avoiding permutations.
- Notes:
- Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
- Advisors: Haglund, Jim; Committee members: Hartmann, Julia; Skandera, Mark.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2022.
- Local Notes:
- School code: 0175
- ISBN:
- 9798834092032
- Access Restriction:
- Restricted for use by site license.
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