A proof of the fermionic theta coinvariant conjecture

Let (x1, ... , xn, y1, ... , yn) be a list of 2n commuting variables, (theta 1, ... , theta n, xi 1, ... , xi n) be a list of 2n anticommuting variables, and C[xn, yn] circle times perpendicular to{On, 4n} be the algebra generated by these variables. D'Adderio, Iraci, and Vanden Wyngaerd introduced the Theta operators on the ring of symmetric functions and used them to conjecture a formula for the quadruply -graded en-isomorphism type of C[xn,yn] circle times perpendicular to{On, 4n}/I where I is the ideal generated by en-invariants with vanishing constant term. We prove their conjecture in the 'purely fermionic setting' obtained by setting the commuting variables xi, yi equal to zero.(c) 2023 Elsevier B.V. All rights reserved.