arXiv subjects
Publications and source records attributed to Sandeep Bhargava.
We study the finite-dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{2n,ρ}(\mathbb{C}_q)$ by investigating the structure of the $\mathrm{BC}_n$-graded Lie algebra $\mathfrak{g}_{2n,ρ}(R)$, where $R$ is a unital involutory associative algebra over a field $k$ of characteristic zero.
We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.
We study intersection matrix algebras im(A^d) that arise from affinizing a Cartan matrix A of type B_r with d arbitrary long roots in the root system $Δ_{B_r}$, where $r \geq 3$. We show that im(A^d) is isomorphic to the universal covering algebra of $so_{2r+1}(a,η,C,χ)$, where $a$ is an associative algebra with involution $η$, and $C$ is an $a$-module with hermitian form $χ$. We provide a description of all four of the components $a$, $η$, $C$, and $χ$.