Foundations of Frobenius Heisenberg categories
Jonathan Brundan, Alistair Savage, Ben Webster
TL;DR
This paper establishes bases for morphism spaces in Frobenius Heisenberg categories linked to symmetric graded Frobenius algebras, proving conjectures and connecting the Grothendieck ring to lattice Heisenberg algebras.
Contribution
It provides a basis theorem for morphism spaces and demonstrates the Grothendieck ring recovers the lattice Heisenberg algebra, advancing understanding of Frobenius Heisenberg categories.
Findings
Proved bases for morphism spaces in Frobenius Heisenberg categories.
Confirmed conjectures related to categorical structures.
Showed the Grothendieck ring recovers the lattice Heisenberg algebra.
Abstract
We describe bases for the morphism spaces of the Frobenius Heisenberg categories associated to a symmetric graded Frobenius algebra, proving several open conjectures. Our proof uses a categorical comultiplication and generalized cyclotomic quotients of the category. We use our basis theorem to prove that the Grothendieck ring of the Karoubi envelope of the Frobenius Heisenberg category recovers the lattice Heisenberg algebra associated to the Frobenius algebra.
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