13 problems

Fusion-product independence conjecture. The corresponding fusion product does not depend on $Z$ as a representation of $\g\otimes\mathbb{C}[u]$.

Let $\widehat{\mathfrak{g}}$ be an affine Kac–Moody algebra, let $\Lambda=m\Lambda_0+\lambda$ be a dominant integral weight, and let $V(\Lambda)$ and $V(\lambda)$ denote the corres…

Let ${\mathfrak{g}}$ be a simple Lie algebra, let $\lambda=\lambda_1+\cdots+\lambda_n$ be a sum of dominant integral weights, and let $c_1,\ldots,c_n$ be pairwise distinct complex…

Let $\lambda^1,\dots,\lambda^n$ be weights, let $W^1(\lambda^i)$ be the level-one Weyl modules, and let $W^1(\lambda^i)^{[k]}$ denote their level-$k$ constructions. Let $*$ denote…

Let ${\mathfrak g}$ be a simple Lie algebra, let $\lambda^1,\dots,\lambda^n$ be weights, let $V(\lambda^i)$ be the corresponding finite-dimensional ${\mathfrak g}$-modules, and let…

Let $\mathfrak{g}$ be a simple Lie algebra, let $k\in\mathbb{Z}_{>0}$, and let $\lambda_s\in P^+$ for $1\leq s\leq k$. For pairwise distinct complex numbers $a_1,\ldots,a_k$ and pa…

Let $A_{(m)}(n)$ be the subalgebra generated by $\xi_0,\ldots,\xi_{n-1}$ in $A_{(m)}$, and let $I_{(m)}(n)$ be its defining ideal. For a family…

Let $W_1,\dots,W_r$ be the modules considered in the preceding construction, let $\mathcal{A}(\lambda_1,\dots,\lambda_r)$ be the associated parameter algebra, and let…

Let $\mathfrak{g}$ be a simple Lie algebra, let $P_{\ell}$ be the set of level-$\ell$ dominant weights, let $W_{\ell}$ be the affine Weyl group, and let $V(\lambda)$ denote the irr…

Let $P^+$ be the dominant integral weights of $cmathfrak{sl}_n$, let $cmathcal{P}_{clambda}$ be the set of decompositions of $clambdain P^+$ into two dominant weights, and let…

Let $cmathfrak{g}$ be a semisimple complex Lie algebra, let $P^+$ denote its dominant integral weights, and fix $clambda_1,clambda_2in P^+$. Put $clambda=clambda_1+clambda_2$, and…

Let $cmathfrak{g}$ be a semisimple complex Lie algebra, let $P^+$ be its dominant integral weights, and let $a_1,\ldots,a_sincmathbb C$ be pairwise distinct with…

Let $P^+$ be the set of dominant integral weights. For $\lambda\in P^+$ and $N\geq1$, let $\operatorname{W}(\lambda,N)$ be the truncated Weyl module for…