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There is a way to characterize for which $x_1,...,x_d$ a Schur polynomial, that can be defined as $$s_\lambda(x_1,...,x_d)=\sum_{T\in SSYT(\lambda)}x_1^{t_1}...x_d^{t_d}, $$ with the sum running over …

Suppose a polynomial of the form $$\prod_i^d \sum_j^p x_i^{f_j}$$ clearly symmetric, where $f_j\in \mathbb{N}$. There is a way to find the set of $f$ numbers such that this polynomial is Schur positiv …

Given the famous Littlewood-Richardson rule, in terms of Schur polynomials: $$s_\mu s_\nu=\sum_\lambda c^{\lambda}_{\mu\nu} s_\lambda,$$ is there a classification of the cases where the LR coefficient …

For a fixed partition $\lambda=(\lambda_1\geq\dots\geq \lambda_n)$ we say $\mu=(\mu_1\geq \dots \geq \mu_{n-1})$ $\textit{interlaces}$ $\lambda$ iff $$\lambda_1\geq \mu_1\geq \dots \geq \mu_{n-1}\geq …

Given that $U(n)$ is a smooth manifold I would like to know if there is a way of building a representation of $\text{Diff}(U(n))$ once you pick a particular (finite dimensional) representation of $U(n …