43 problems

For $i\in I$ and $\alpha\in J_i$, let $b(i,\alpha)$ be the quantity defined by … where $M^j=a_{\beta\otimes 1}$. Kac–Wakimoto conjecture. One has … for $\alpha\in J_i$. The conject…

Let $\mathfrak{g}$ be a symmetrizable Kac–Moody algebra of affine type, let $L(\lambda)$ be an integrable highest weight representation of $\mathfrak{g}$, and let $\mu$ be a domina…

Let $A$ be a local deformation algebra, let $\mathcal{J}$ be an open and bounded subset of $\widehat{\mathfrak{h}}^*$, and let $\lambda,\mu\in\mathcal{J}$ be of critical level. Wri…

Let $G$) and $\mathfrak g$ be the affine Kac–Moody group and algebra associated with a generalized Cartan matrix, let $I$ be its index set, and let $W(\varpi_i)$ be the fundamental…

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

Let $\mathfrak g_0$ be the finite-dimensional Lie algebra associated with a simply folded full heap over an untwisted affine Dynkin diagram, and let the corresponding representatio…

Let $\mathfrak g$ be an affine Kac–Moody algebra with index set $I$, distinguished node $0$, Weyl group $W$, extended Weyl group $\widetilde W$, and Langlands dual $\mathfrak g^L$.…

Let $\hg$ be an affine Kac–Moody algebra at the critical level, let $\hg_\crit\operatorname{mod}_\nilp^{I,m}$ be the full subcategory of $I$-monodromic $\hg_\crit$-modules supporte…

Let $G$ be a semisimple algebraic group, let $\sigma$ be a local Langlands parameter, and let $\C_\sigma$ be the category associated to $\sigma$. Let $\hg$ be the affine Kac–Moody…

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…

A stable one-dimensional sum is the large-rank limit of the graded tensor-product multiplicities associated with a nonexceptional family of affine algebras. The four stable types a…

The restricted Kostka polynomial conjecture. This definition of the restricted Kostka polynomials coincides with the definition in Kerov, Kirillov and Reshetikhin's work, as far as…

Let $\hat\fg_{crit}\text{--}\on{mod}^{G(\wh{\CO}_x)}_{\nil}$ be the category of $G(\CO_x)$-integrable critical-level $\hat\fg$-modules that are set-theoretically supported on…

Let $G$ be a connected simple algebraic group with Lie algebra $\fg$, let $\LG$ and $\Lg$ be its dual group and dual Lie algebra, and let $\nabla$ be a formal $\LG$-connection on…

Affine vertex algebra–small quantum group correspondence conjecture. The category … associated with $$ .

Isomorphism conjecture. The homomorphism $\pi_H$ is always an isomorphism.

Let $\mathfrak{g}$ be an untwisted affine Kac–Moody Lie algebra, let $\rho$ be the affine Weyl weight used in the tensor product $V(\rho)\otimes V(\rho)$, and let…

Let $\mathfrak{g}$ be an untwisted affine Kac–Moody Lie algebra, let $\delta$ be its null root, and let $\lambda\in\mathcal{P}^+$ be a dominant integral weight of positive level. F…

Let $\mathfrak g=A_n^{(1)}$, let $\Lambda_0$ be the zeroth fundamental weight, and let $\mx^+(\ell\Lambda_0)$ denote the set of dominant maximal weights of the irreducible highest…

Let $\mathfrak{g}=A_{n}^{(1)}$, and let simple basic strategies be the strategies defined from monotonously ordered root partitions of $\theta=\alpha_{1}+\cdots+\alpha_{n}$, togeth…

Let $\mathfrak{g}$ be an affine Kac–Moody algebra, let $V$ be a weight module, and let $\mathfrak{C}$ be the set of normal quasicones arising as annihilators of vectors in $V$. Let…

Let $\mathfrak{g}$ be an affine Kac–Moody algebra and let $V$ be an irreducible weight module. A module is non-dense when its support is a proper subset of a coset of the root latt…

Let $\mathfrak{g}$ be an affine Kac–Moody algebra, and let $V$ be a weight $\mathfrak{g}$-module. The module is non-dense when its support is a proper subset of a coset $\lambda+Q$…

Let $\mathfrak{g}$ be an affine Kac–Moody algebra with Cartan subalgebra $\mathfrak{h}$, root system $\Delta$, center $\mathbb{C}c$, and root lattice $Q$ generated by $\Delta$. A w…

Let $\mathfrak{g}$ be a reductive simply-laced Lie algebra, let $n$ be a positive integer, and let $P^+_n$ be the set of dominant integral weights $\lambda$ of $\mathfrak{g}$ such…