论文标题
费米尼克theta共同猜想的证明
A proof of the fermionic Theta coinvariant conjecture
论文作者
论文摘要
令$（x_1，\ dots，x_n，y_1，\ dots，y_n）$为$ 2N $通勤变量的列表，$（θ_1，\ dots，tin，θ_n，θ_n，ξ_1，dots，dots，ξ_n）$是$ 2n $ and variable and $ n $ n y y MATH y MATH y MATH y MALTIAL y MATH y MALTIAL y MALTIAL y MALTIAB y MATH YMANBB { \ otimes \ wedge \ {θ_n，ξ_n\} $是这些变量生成的代数。 D'Adderio，Iraci和Vanden Wyngaerd在对称函数的环上介绍了{\ em Theta操作员}，并用它们来猜测Quadruply级别的$ \ Mathfrak {s} _n $ isomorphism $ isomorphism $ \ mathbbbb {y__n]的公式\ {θ_n，ξ_n\}/i $，其中$ i $是$ \ mathfrak {s} _n $ invariants生成的理想，具有消失的常数。我们通过将通勤变量等于$ x_i，y_i $等于零来证明他们在“纯粹的费米子设置”中的猜想。
Let $(x_1, \dots, x_n, y_1, \dots, y_n)$ be a list of $2n$ commuting variables, $(θ_1, \dots, θ_n, ξ_1, \dots, ξ_n)$ be a list of $2n$ anticommuting variables, and $\mathbb{C}[X_n, Y_n] \otimes \wedge \{Θ_n, Ξ_n\}$ be the algebra generated by these variables. D'Adderio, Iraci, and Vanden Wyngaerd introduced the {\em Theta operators} on the ring of symmetric functions and used them to conjecture a formula for the quadruply-graded $\mathfrak{S}_n$-isomorphism type of $\mathbb{C}[X_n,Y_n] \otimes \wedge \{Θ_n, Ξ_n\}/I$ where $I$ is the ideal generated by $\mathfrak{S}_n$-invariants with vanishing constant term. We prove their conjecture in the `purely fermionic setting' obtained by setting the commuting variables equal $x_i, y_i$ equal to zero.
