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Semi-invariants of Finite Reflection Groups

✍ Scribed by Anne V Shepler

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
99 KB
Volume
220
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let G be a finite group of complex n = n unitary matrices generated by reflections acting on ‫ރ‬ n . Let R be the ring of invariant polynomials, and let be a multiplicative character of G. Let ⍀ be the R-module of -invariant differential forms. We define a multiplication in ⍀ and show that under this multiplication ⍀ has an exterior algebra structure. We also show how to extend the results to vector fields, and exhibit a relationship between -invariant forms and logarithmic forms.

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