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Weil representations of unitary groups over ramified extensions of finite local rings with odd nilpotency length
We find the irreducible decomposition of the Weil representation of the unitary group U2n(A), where A is a ramified quadratic extension of a finite, commutative, local, principal ideal ring R and the nilpotency degree of the maximal ideal of A is odd. We show in particular that this Weil representation …