Real-valued and 2-rational group characters
نویسندگان
چکیده
منابع مشابه
Shintani lifting and real-valued characters
We study Shintani lifting of real-valued irreducible characters of finite reductive groups. In particular, if G is a connected reductive group defined over Fq, and ψ is an irreducible character of G(Fqm) which is the lift of an irreducible character χ of G(Fq), we prove ψ is real-valued if and only if χ is real-valued. In the case m = 2, we show that if χ is invariant under the twisting operato...
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We prove that the duality operator preserves the Frobenius–Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius–Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius–Schur indicators of certain real-valued, i...
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Let E be an elliptic curve over Q with complex multiplication by the ring of integers of an imaginary quadratic eld. Let be the Hecke character associated to E by the theory of complex multiplication. Let be the complex conjugate character of. For a pair of integers k and j, deene the Hecke character ' = '(k; j) = k j. Let p be a prime where E has good, ordinary reduction. Let p be a xed prime ...
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The group ? of automorphisms of the polynomial is isomorphic to PGL(2; Z)n (Z=2 Z=2). We study the dynamics of the ?-action on ?1 (t) \ R 3 , for t 2 R. The action of ? preserves a Poisson structure deening a ?-invariant area form on each ?1 (t) \ R 3. For t < 2, the action of ? is properly discontinuous on the four contractible components of ?1 (t) \ R 3 and ergodic on the compact component (w...
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is isomorphic to PGL(2,Z)⋉ (Z/2⊕ Z/2). For t ∈ R , the Γ-action on κ(t) ∩ R displays rich and varied dynamics. The action of Γ preserves a Poisson structure defining a Γ–invariant area form on each κ(t) ∩ R . For t < 2, the action of Γ is properly discontinuous on the four contractible components of κ(t) ∩R and ergodic on the compact component (which is empty if t < −2). The contractible compon...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1979
ISSN: 0021-8693
DOI: 10.1016/0021-8693(79)90288-6