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0-Hecke algebras

  • P. N. Norton (a1)

Abstract

The structure of a 0-Hecke algebra H of type (W, R) over a field is examined. H has 2n distinct irreducible representations, where n = ∣R∣, all of which are one-dimensional, and correspond in a natural way with subsets of R. H can be written as a direct sum of 2n indecomposable left ideals, in a similar way to Solomon's (1968) decomposition of the underlying Coxeter group W.

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References

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Bourbaki, N. (1968), Groupes et algèbres de Lie, Chapitres 4, 5 et 6 (Hermann, Paris).
Carter, R. W. (1972), Simple groups of Lie type (John Wiley and Sons, New York).
Curtis, C. W. and Reiner, I. (1962), Representation theory of finite groups and associative algebras (Interscience Publishers, New York).
Dornhoff, L. (1972), (Group representation theory, Part B. Marcel Decker, Inc., New York).
Solomon, L. (1968), ‘A decomposition of the group algabra of a finite Coxeter group’, J. Algebra, 9, 220239.
Steinberg, R. (1967), Lectures on Chevalley groups (Yale University).
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