Compound Basis Arising from the Basic {A^{(1)}_{1}}-Module

Given a conditionally completely positive map on a unital *-algebra , we find an interesting connection between the second Hochschild cohomology of with coefficients in the bimodule of adjointable maps, where M is the GNS bimodule of , and the possibility of constructing a quantum random walk [in the sense of (Attal et al. in Ann Henri Poincar 7(1):59–104, 2006; Lindsay and Parthasarathy in Sankhya Ser A 50(2):151–170, 1988; Sahu in Quantum stochastic Dilation of a class of Quantum dynamical Semigroups and Quantum random walks. Indian Statistical Institute, 2005; Sinha in Banach Center Publ 73:377–390, 2006)] corresponding to . D. Goswami was supported by a project funded by the Indian National Academy of Sciences. L. Sahu had research support from the National Board of Higher Mathematics, DAE (India) is gratefully acknowledged.     

Pfaffian identities and Virasoro operators

Letters in Mathematical Physics - A formula for Schur Q-functions is presented which describes the action of the Virasoro operators. For a strict partition $$\lambda =(\lambda _1,\lambda _2,\ldots...     

Tensor square of the basic spin representations of Schur covering groups for the symmetric groups

Journal of Algebraic Combinatorics - We consider the tensor square of the basic spin representations of Schur covering groups $$\widetilde{S_n}$$ and $$\widetilde{S_n^{'}}$$ for the symmetric...