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

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CRC Handbook of Combinatorial Designs

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.

Linear Algebraic Groups

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.

http://inis.jinr.ru/sl/M_Mathematics/MA_Algebra/MAtg_Group%20theory/Gorenstein%20D.,%20Lyons%20R.,%20Solomon%20R.%20Classification%20of%20finite%20simple%20groups%201%20(AMS%20survey%2040%20no.1,%201994,%202000)(176s).pdf

The Classification of the Finite Simple Groups

On Whittaker vectors and representation theory

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Handbook of magma functions

Lectures on Lie Groups and Lie Algebras: Homogeneous spaces and quotients

Let U be the quantum group associated to a Lie algebra g of rank n. The negative part U^- of U has a canonical basis B with favourable properties, introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in the Weyl group of g. We describe the authors' recent work establishing close relationships between the Lusztig cones, canonical basis elements and the regions of linearity of reparametrization functions arising from the above parametrizations in type A_4 and give some speculations for type A_n. 
Keywords: Quantum group, Lie algebra, Canonical basis, Tight monomials, Weyl group, Piecewise-linear functions.

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Roger W. Carter

Papers

Lectures on Lie Groups and Lie Algebras: Homogeneous spaces and quotients

Canonical Bases and Piecewise-linear Combinatorics