Titlebook: Compact Lie Groups; Mark R. Sepanski Textbook 2007 Springer-Verlag New York 2007 Group theory.Lie algebra.Representation theory.algebra.ca

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HarmoniC Analysis,Throughout this chapter let . be a . Lie group. This chapter studies a number of function spaces on . such as the set of continuous functions on ., or the set of square integrable functions on ., with respect to the Haar measure .. These function spaces are examined in the light of their behavior under left and right translation by ..

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兽群

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Abelian Lie Subgroups and Structure,tion in .. In fact, the main theorem of this chapter shows it is possible to diagonalize each . ∃ . using conjugation in .. This result will have far-reaching consequences, including various structure theorems.

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Highest Weight Theory, Two important problems remain. The first is to parametrize Ĝ in a reasonable manner and the second is to individually construct each irreducible representation in a natural way. The solution to both of these problems is closely tied to the notion of . weights.

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Emotions as Situated, Embodied, and Fissured: Methodological Implications of Thinking with Theoriesr concludes with discussions about disrupting traditional ways of studying emotions, expanding theoretical and philosophical assumptions about emotions and how that shapes methodological actions, and creating different approaches of thinking-with-theories rather than reductionist codes for analysis.