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Affine and cyclotomic Brauer categorification via -Kac--Moody -categories: the half-integral type case
Mengmeng Gao, Hebing Rui, Linliang Song
Cyclotomic Brauer or cyclotomic Nazarov--Wenzl algebras arise in higher Schur--Weyl dualities involving parabolic categories for Lie algebras of types and . T…
Decomposition numbers of cyclotomic Brauer algebras over the complex field, I
Mengmeng Gao, Hebing Rui
Following Nazarov's suggestion~\cite{Naz1}, we refer to the cyclotomic Nazarov-Wenzl algebra as the cyclotomic Brauer algebra. When the cyclotomic Brauer algebra is isomorphic to t…
Blocks of the Brauer category over the complex field
Mengmeng Gao, Hebing Rui, Linliang Song
Let be the Brauer category over the complex field with the parameter . In non-semisimple case, is an integer, and each weight space of $(\fracδ2-…
Representations of cyclotomic oriented Brauer categories
Mengmeng Gao, Hebing Rui, Linliang Song
Let be the locally unital algebra associated to a cyclotomic oriented Brauer category over an arbitrary algebraically closed field of characteristic . The categ…
Representations of weakly triangular categories
Mengmeng Gao, Hebing Rui, Linliang Song
A new class of locally unital and locally finite dimensional algebras over an arbitrary algebraically closed field is discovered. Each of them admits an upper finite weakly tri…
A basis theorem for the affine Kauffmann category and its cyclotomic quotients
Mengmeng Gao, Hebing Rui, Linliang Song
The affine Kauffmann category is a strict monoidal category and can be considered as a -analogue of the affine Brauer category in (Rui et al. in Math. Zeit. 293, 503-550, 2019).…