Geodesic
Peter–Weyl Iwahori Algebras
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1304-1323

Voir la notice de l'article provenant de la source Cambridge University Press

The Peter–Weyl idempotent $e_{\mathscr{P}}$ of a parahoric subgroup $\mathscr{P}$ is the sum of the idempotents of irreducible representations of $\mathscr{P}$ that have a nonzero Iwahori fixed vector. The convolution algebra associated with $e_{\mathscr{P}}$ is called a Peter–Weyl Iwahori algebra. We show that any Peter–Weyl Iwahori algebra is Morita equivalent to the Iwahori–Hecke algebra. Both the Iwahori–Hecke algebra and a Peter–Weyl Iwahori algebra have a natural conjugate linear anti-involution $\star$, and the Morita equivalence preserves irreducible hermitian and unitary modules. Both algebras have another anti-involution, denoted by $\bullet$, and the Morita equivalence preserves irreducible and unitary modules for $\bullet$.
DOI : 10.4153/S0008414X19000324
Mots-clés : convolution algebra, Iwahori–Hecke algebra, idempotent, Morita equivalence, parahoric subgroup, Peter–Weyl idempotent, ⋆-algebra 
Barbasch, Dan; Moy, Allen. Peter–Weyl Iwahori Algebras. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1304-1323. doi: 10.4153/S0008414X19000324
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