5 problems

Let $k$ be a positive integer, let $\mathcal{Z}\mathcal{V}_k$ be the coset-type-constant subspace, let $\mathfrak{p}_\lambda$ be the $b$-deformed class vector for $\lambda\vdash k$…

Let $k$ be a positive integer, let $\mathcal{Z}\mathcal{V}_k$ be the subspace of vectors constant on coset-type, and let $\mathfrak{p}_\lambda,\mathfrak{w}_\lambda$ be the $b$-defo…

Let $k$ be a positive integer, let $\mathcal{J}_1,\ldots,\mathcal{J}_k$ be the $b$-deformed Jucys–Murphy operators, and let $\mathfrak{e}_k$ be the identity pair partition. Define…

McNamara's center conjecture. The center $Z(\mathscr{H}_{n,K}^\Lambda)$ is precisely the set of symmetric polynomials in $\mathcal{L}_1,\ldots,\mathcal{L}_n$.

Let $\alpha$ be fixed, let $\rho$ be a partition, and let $a_{\rho}^{k,(\alpha)}$ be the coefficients defined by … For a partition $\rho$, write $\rho\cup(m)$ for adjoining a part…