Types and unitary representations of reductive p-adic groups
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DOI: 10.1007/s00222-018-0790-4
Abstract: We prove that for every Bushnell–Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces… read more here.
Keywords: representations reductive; adic groups; unitary representations; types unitary ... See more keywords
Inductive limits of compact quantum groups and their unitary representations
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DOI: 10.1007/s11005-021-01468-0
Abstract: We will introduce the notion of inductive limits of compact quantum groups as $W^*$-bialgebras equipped with some additional structures. We also formulate their unitary representation theories. Those give a more explicit representation-theoretic meaning to our… read more here.
Keywords: inductive limits; unitary representations; quantum groups; compact quantum ... See more keywords
Unitary representations of three dimensional Lie groups revisited: A short tutorial via harmonic functions
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DOI: 10.1016/j.geomphys.2017.01.004
Abstract: Abstract The representation theory of three dimensional real and complex Lie groups is reviewed from the perspective of harmonic functions defined over certain appropriate manifolds. An explicit construction of all unitary representations is given. The… read more here.
Keywords: three dimensional; harmonic functions; unitary representations; lie groups ... See more keywords
Current superalgebras and unitary representations
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DOI: 10.1016/j.jpaa.2017.12.009
Abstract: In this paper we determine the projective unitary representations of finite dimensional Lie supergroups whose underlying Lie superalgebra is $\frak{g} = A \otimes \frak{k}$, where $\frak{k}$ is a compact simple Lie superalgebra and $A$ is… read more here.
Keywords: lie; projective unitary; unitary representations; current superalgebras ... See more keywords
Projective unitary representations of infinite-dimensional Lie groups
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DOI: 10.1215/21562261-2018-0016
Abstract: For an infinite dimensional Lie group $G$ modelled on a locally convex Lie algebra $\mathfrak{g}$, we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie… read more here.
Keywords: lie; projective unitary; unitary representations; infinite dimensional ... See more keywords
Unitary representations with non-zero Dirac cohomology for complex E 6
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DOI: 10.1515/forum-2018-0132
Abstract: Abstract This paper classifies the equivalence classes of irreducible unitary representations with non-vanishing Dirac cohomology for complex E 6 {E_{6}} . This is achieved by using our finiteness result, and by improving the computing method.… read more here.
Keywords: non zero; dirac cohomology; cohomology complex; representations non ... See more keywords