Zelevinski algebras related to projective representations
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- by M. Bean and P. Hoffman PDF
- Trans. Amer. Math. Soc. 309 (1988), 99-111 Request permission
Abstract:
We define $L$-$\operatorname {PSH}$-algebras, and prove a classification theorem for such objects. The letters refer respectively to a ground ring $L$ and to the positivity, selfadjointness and Hopf structures on an algebra, the basic example of which occurred in the study of projective representations of ${S_n}$. This is analogous to an idea over ${\mathbf {Z}}$ due to Zelevinski in connection with linear representations.References
- Peter Hoffman, $\tau$-rings and wreath product representations, Lecture Notes in Mathematics, vol. 746, Springer, Berlin, 1979. MR 549031
- Peter N. Hoffman and John F. Humphreys, Hopf algebras and projective representations of $G\wr S_n$ and $G\wr A_n$, Canad. J. Math. 38 (1986), no. 6, 1380–1458. MR 873418, DOI 10.4153/CJM-1986-070-1 —, Projective representations of generalized symmetric groups using $PSH$-algebras (to appear).
- Arunas Liulevicius, Arrows, symmetries and representation rings, J. Pure Appl. Algebra 19 (1980), 259–273. MR 593256, DOI 10.1016/0022-4049(80)90103-6
- Andrey V. Zelevinsky, Representations of finite classical groups, Lecture Notes in Mathematics, vol. 869, Springer-Verlag, Berlin-New York, 1981. A Hopf algebra approach. MR 643482
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 309 (1988), 99-111
- MSC: Primary 20C25; Secondary 20C30
- DOI: https://doi.org/10.1090/S0002-9947-1988-0957063-3
- MathSciNet review: 957063