References & Citations
Mathematics > Combinatorics
Title: Rotation invariant webs for three row flamingo Specht modules
(Submitted on 19 Feb 2024 (v1), last revised 25 Apr 2024 (this version, v3))
Abstract: We introduce a new rotation-invariant web basis for a family of Specht modules $S^{(d^3, 1^{n-3d})}$, indexed by normal plabic graphs satisfying a degree condition and resembling $A_2$ webs. We show that the $\mathfrak{S}_n$ action on our basis can be understood combinatorially via a set of skein relations. From this basis, we obtain a cyclic sieving result for a $q$-analog of the hook length formula for $\lambda$. Our construction extends the jellyfish invariants of Fraser, Patrias, Pechenik, and Striker and is closely related to the weblike subgraphs of Lam.
Submission history
From: Jesse Kim [view email][v1] Mon, 19 Feb 2024 09:39:15 GMT (38kb)
[v2] Wed, 21 Feb 2024 05:53:35 GMT (40kb)
[v3] Thu, 25 Apr 2024 00:56:03 GMT (41kb)
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