Not necessarily continuous locally bounded finite-dimensional representations of connected Lie groups with indecomposable restriction to the radical
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Since an analog of the Weyl complete reducibility theorem for not necessarily continuous representations of connected Lie groups is now known, we consider the “opposite” case and find (in terms of representations of the radical and a Levi subgroup of the group) an explicit form for every (not necessarily continuous) locally bounded finite-dimensional representation of a connected Lie group whose restriction to the radical is indecomposable.
Abstract
Since an analog of the Weyl complete reducibility theorem for not necessarily continuous representations of connected Lie groups is now known, we consider the “opposite” case and find (in terms of representations of the radical and a Levi subgroup of the group) an explicit form for every (not necessarily continuous) locally bounded finite-dimensional representation of a connected Lie group whose restriction to the radical is indecomposable.
참고문헌 (6)
- A. I. Shtern, "A Version of the Weyl Complete Reducibility Theorem for Not Necessarily Continuous Representations of Connected Lie Groups", Russ. J. Math. Phys, 26(1), pp.75~76 (2019)
- A. I. Shtern, "Continuity Conditions for Finite-Dimensional Locally Bounded Representations of Connected Locally Compact Groups", Russ. J. Math. Phys, 25(3), pp.345~382 (2018)
- A. I. Shtern, "Not necessarily continuous locally bounded finite-dimensional irreducible representations of connected lie groups", Advanced Studies in Contemporary Mathematics, 29(1), pp.1~5 (2019), 장전수학회[DOI]
- A. I. Shtern, "Finite-dimensional quasi-representations of connected Lie groups and Mishchenko’s conjecture", J. Math. Sci, 159(5), pp.653~751 (2009)
- A. I. Shtern, "REMARKS ON FINITE-DIMENSIONAL LOCALLY BOUNDED FINALLY PRECONTINUOUS QUASIREPRESENTATIONS OF LOCALLY COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 20(4), pp.469~480 (2010), 장전수학회
- A. I. Shtern, "A version of van der Waerden’s theorem and a proof of Mishchenko’s conjecture on homomorphisms of locally compact groups", Izv. Math, 72(1), pp.169~205 (2008)