Abstract
In this chapter we develop some algebraic tools needed for the general theory of representations and invariants. The central result is a duality theorem for locally regular representations of a reductive algebraic group G. The duality between the irreducible regular representations of G and irreducible representations of the commuting algebra of G plays a fundamental role in classical invariant theory. We study the representations of a finite group through its group algebra and characters, and we construct induced representations and calculate their characters.
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© 2009 Springer-Verlag New York
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Goodman, R., Wallach, N.R. (2009). Algebras and Representations. In: Symmetry, Representations, and Invariants. Graduate Texts in Mathematics, vol 255. Springer, New York, NY. https://doi.org/10.1007/978-0-387-79852-3_4
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DOI: https://doi.org/10.1007/978-0-387-79852-3_4
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-79851-6
Online ISBN: 978-0-387-79852-3
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