Roger W. Carter

Bio: Roger W. Carter is an academic researcher from University of Warwick. The author has contributed to research in topics: Lie algebra & Group of Lie type. The author has an hindex of 16, co-authored 22 publications receiving 4324 citations. Previous affiliations of Roger W. Carter include University of Cambridge.

Finite Groups of Lie Type: Conjugacy Classes and Complex Characters

Abstract: BN-Pairs and Coxeter Groups. Maximal Tori and Semisimple Classes. Geometric Conjugacy and Duality. Unipotent Classes. The Steinberg Character. The Generalized Characters of Deligne-Lusztig. Further Families of Irreducible Characters. Cuspidal Representations. The Decomposition of Induced Cuspidal Characters. Representations of Finite Coxeter Groups. Unipotent Characters. Explicit Results on Simple Groups. Appendix. Bibliography. Indexes.

Lie Algebras of Finite and Affine Type

Abstract: 1. Basic concepts 2. Representations of soluble and nilpotent Lie algebras 3. Cartan subalgebras 4. The Cartan decomposition 5. The root systems and the Weyl group 6. The Cartan matrix and the Dynkin diagram 7. The existence and uniqueness theorems 8. The simple Lie algebras 9. Some universal constructions 10. Irreducible modules for semisimple Lie algebras 11. Further properties of the universal enveloping algebra 12. Character and dimension formulae 13. Fundamental modules for simple Lie algebras 14. Generalized Cartan matrices and Kac-Moody algebras 15. The classification of generalised Cartan matrices 16 The invariant form, root system and Weyl group 17. Kac-Moody algebras of affine type 18. Realisations of affine Kac-Moody algebras 19. Some representations of symmetrisable Kac-Moody algebras 20. Representations of affine Kac-Moody algebras 21. Borcherds Lie algebras Appendix.

On the modular representations of the general linear and symmetric groups

Abstract: Let V be an n-dimensional vector space over C with basis X 1, X 2,..., X n and let T r = V ⊗ V ⊗ ... ⊗ V (r factors). T r is a module both for GL n (C), via its action on V, and for the symmetric group S r by place permutations.

Lectures on Lie groups and Lie algebras

Abstract: In this excellent introduction to the theory of Lie groups and Lie algebras, three of the leading figures in this area have written up their lectures from an LMS/SERC sponsored short course in 1993 Together these lectures provide an elementary account of the theory that is unsurpassed In the first part Roger Carter concentrates on Lie algebras and root systems In the second Graeme Segal discusses Lie groups And in the final part, Ian Macdonald gives an introduction to special linear groups Anybody requiring an introduction to the theory of Lie groups and their applications should look no further than this book

CRC Handbook of Combinatorial Designs

Abstract: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex

Linear Algebraic Groups

Abstract: A linear algebraic group over an algebraically closed field k is a subgroup of a group GL n (k) of invertible n × n-matrices with entries in k, whose elements are precisely the solutions of a set of polynomial equations in the matrix coordinates. The present article contains a review of the theory of linear algebraic groups.

The Classification of the Finite Simple Groups

Abstract: General introduction to the special odd case General lemmas Theorem $C^*_2$: Stage 1 Theorem $C^*_2$: Stage 2 Theorem $C_2$: Stage 3 Theorem $C_2$: Stage 4 Theorem $C_2$: Stage 5 Theorem $C_3$: Stage 1 Theorem $C_3$: Stages 2 and 3 IV$_K$: Preliminary properties of $K$-groups Background references Expository references Glossary Index.