10 problems

The generalised blob algebras arise as transfer matrix algebras for one-boundary Potts models in statistical mechanics. Their representation-theoretic structure is expected to be g…

Let $\Lambda_n$ be the indexing set of weights, let $W$ be the relevant Weyl group, and let $\mathcal{A}^w$ denote the orbit or alcove associated with $w\in W$. For…

Let $l>2$, let ${\boldsymbol{\lambda}}$ and ${\boldsymbol{\mu}}$ be weights for the level $l$ generalised blob algebra over a field of characteristic $0$, and for each weight let…

Let $l>2$ and let ${\boldsymbol{\lambda}},{\boldsymbol{\mu}}$ be regular one-column $l$-multipartitions. Consider the level $l$ generalised blob algebra over a field $\Bbbk$ of cha…

Let $P_1^l(n)$ be the set of $l$-tuples of non-negative integers summing to $n$, and let $P(\boldsymbol{\lambda})$ denote the orbit of $\boldsymbol{\lambda}$. For a regular…

Let $P_1^l(n)$ be the set of $l$-tuples of non-negative integers summing to $n$. Let $\boldsymbol{\lambda},\boldsymbol{\mu}\in P_1^l(n)$ be regular, with $\boldsymbol{\mu}$ in the…

Let $p$ be the characteristic of the ground field, and let $d^p_{\boldsymbol{\lambda},\boldsymbol{\mu}}(v)$ denote the graded decomposition numbers of a generalized blob algebra, w…

Let $p$ be a prime, let $l\geq 2$, and fix the data $(e,l,n,\kappa)$ of a generalized blob algebra. For a regular $\boldsymbol{\lambda}\in P_1^l(n)$, let…

Let the generalised blob algebras be the finite-rank algebras considered in the paper's comparison, and let the associated Kazhdan–Lusztig polynomials be those governing the graded…

The paper considers quiver Temperley–Lieb algebras of type $G(l,1,n)$ arising as saturated quotients of Webster's algebra for a FLOTW weighting, with standard modules indexed by on…