Abstract
In this paper, we study the incidence algebra T of the attenuated space poset Aq(N,M). We consider the following topics. We consider some generators of T: the raising matrix R, the lowering matrix L, and a certain diagonal matrix K. We describe some relations among R,L,K. We put these relations in an attractive form using a certain matrix S in T. We characterize the center Z(T). Using Z(T), we relate T to the quantum group Uτ(sl2) with τ2=q. We consider two elements A,A⁎ in T of a certain form. We find necessary and sufficient conditions for A,A⁎ to satisfy the tridiagonal relations. Let W denote an irreducible T-module. We find necessary and sufficient conditions for the above A,A⁎ to act on W as a Leonard pair.
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