NOT NECESSARILY CONTINUOUS LOCALLY BOUNDED FINALLY PRECONTINUOUS FINITE-DIMENSIONAL IRREDUCIBLE REPRESENTATIONS OF CONNECTED LOCALLY COMPACT GROUPS
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참고문헌
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초록
We obtain an explicit form of every (not necessarily continuous) locally bounded finally precontinuous finite-dimensional representation of a connected locally compact group in terms of representations of the radical and a Levi subgroup of the quotient Lie group of the locally compact group by a normal subgroup whose image under the representation is contained in a ball of radius less than one centered at the identity operator in the representation space.
Abstract
We obtain an explicit form of every (not necessarily continuous) locally bounded finally precontinuous finite-dimensional representation of a connected locally compact group in terms of representations of the radical and a Levi subgroup of the quotient Lie group of the locally compact group by a normal subgroup whose image under the representation is contained in a ball of radius less than one centered at the identity operator in the representation space.
참고문헌 (8)
- A. O. Barut, "Theory of Group Representations and Applications" (1986), World Scientific Publishing Co.
- 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, "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, "Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups", Mat. Sb, 208(10), pp.149~170 (2017)
- 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)
- L. S. Pontryagin, "Topological Groups" (1973), Izdat. “Nauka”