Alladi Ramakrishnan Hall

Combinatorial Structures and Correspondence in Walled Klein-4 Brauer Algebra

S. Dhilshath

University of Madras

In this talk, we introduce a new class of diagram algebra: the walled
Klein-4 Brauer algebra. This algebra is explored through its generators and
relations, and we detail the indexing set of its simple modules.
Additionally, we establish the Robinson-Schensted correspondence for the
walled Klein-4 Brauer algebra, constructing a bijection between the set of
all walled Klein-4 Brauer diagrams and pairs of Klein-4 vacillating
tableaux.