Multiplicity-free permutation representations of finite linear groups

DOI10.1007/BF01164008zbMath0578.20006OpenAlexW1987409291MaRDI QIDQ1066258

Martin W. Liebeck, Nicholas F. J. Inglis, Jan Saxl

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173737

zbMATH Keywords

finite simple groupsautomorphism groupsirreducible characterspermutation characterdistance-transitive graphsprimitive multiplicity- free permutation representations

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Finite simple groups and their classification (20D05)

Related Items (17)

Finite distance-transitive generalized polygons ⋮ The Multiplicity Free Permutation Representations of the Ree Groups²G₂(q), the Suzuki Groups²B₂(q), and Their Automorphism Groups ⋮ Trees, wreath products and finite Gelfand pairs ⋮ Statistical enumeration of groups by double cosets ⋮ Stein's method, heat kernel, and linear functions on the orthogonal groups ⋮ Distance-transitive representations of the sporadic groups ⋮ The decomposition of the permutation character \(1^{\text{GL}(2n,q)}_{\text{GL}(n,q^2)}\) ⋮ Irreducibility of unitary group representations and reproducing kernels Hilbert spaces. Appendix on two point homogeneous compact ultrametric spaces in collaboration with Rostislav Grigorchuk. ⋮ On distance transitive graphs whose automorphism groups are affine ⋮ Degrees of rational characters of finite groups. ⋮ On imprimitive multiplicity-free permutation groups the degree of which is the product of two distinct primes. ⋮ Multiplicity-free representations of symmetric groups. ⋮ Distance-transitive representations of groups G with \(PSL_ 2(q)\trianglelefteq G\leq P\Gamma L_ 2(q)\) ⋮ Linear groups and distance-transitive graphs ⋮ Cuspidal representations associated to \((\text{GL}(n),O(n))\) over finite fields and \(p\)-adic fields ⋮ Mackey's theory of \(\tau\)-conjugate representations for finite groups. ⋮ Appendix: On some Gelfand pairs and commutative association schemes.

Cites Work

• 2-transitive and antiflag transitive collineation groups of finite projective spaces
• On the maximal subgroups of the finite classical groups
• Line-transitive collineation groups of finite projective spaces
• On Graphs Whose Full Automorphism Group is an Alternative Group or a Finite Classical Group
• On the Orders of Maximal Subgroups of the Finite Classical Groups
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