#### 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.

Done