5 papers
Categorification of generic Su-Zhang character formula
Shunsuke Hirota
For semisimple Lie algebras, the BGG resolution is often viewed as a categorification of the Weyl character formula. For general linear Lie superalgebras, Brundan--Stroppel constru…
-Verma -dual Verma supermodules
Shunsuke Hirota
We show that if a module M over a basic classical Lie superalgebra of type type I is simultaneously a Verma module with respect to some Borel \(\mathfrak b_1\) and a dual Verma mod…
Rainbow Boomerang Graphs
Shunsuke Hirota
We generalize the well known exchange property of Coxeter groups to the setting of edge-colored graphs. This work aims to unify and extend the results of our companion article, "od…
Odd Verma's Theorem
Shunsuke Hirota
We formulate several basic properties of Verma supermodules over regular symmetrizable Kac--Moody Lie superalgebras, exhibiting -nature as revealed through chan…
Hypercubic Decomposition of Verma Supermodules and Semibricks Realizing the Khovanov Algebra of Defect One
Shunsuke Hirota
We study some variants of Verma modules of basic Lie superalgebras obtained via changing Borel subalgebras. These allow us to demonstrate that the principal block of \(\mathfrak{gl…