arXiv · math/0403171
We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.
Philippe Biane, Philippe Bougerol, Neil O'Connell. 2005-01-11. Littelmann paths and brownian paths. https://arxiv.org/abs/math/0403171
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In this paper, we develop a general theory of quasi-Whittaker supermodules over Lie superalgebras induced from an arbitrary ideal. We determine the quasi-Whittaker vectors in universal supermodules, establish an irreducibility criterion, and classify several families of irreducible supermodules. The odd part produces a new irreducibility phenomenon absent from the Lie algebra setting. As applications, we determine all irreducible quasi-Whittaker supermodules over the $N=1$ super Schr\"odinger algebra and the $N=1$ $\frac{3}{2}$-conformal Galilei superalgebra, and over the complete spectrum-generating superalgebra in a special case.
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