#### Alladi Ramakrishnan Hall

#### Wreath product action on generalized Boolean algebras

#### Ashish Mishra

##### IIT Bombay

*Let $G$ be a finite group acting on the finite set $X$ such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product $G wreath S_n$ on the generalized Boolean algebra $B_X(n)$. We explicitly block diagonalize the commutant of this action. To achieve our goal, we explain and use explicit block diagonalization of the commutant of the natural action of $S_n$ on Boolean algebra $B(n)$. This is joint work with Prof. Murali K. Srinivasan.*

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