408 Index

subrepresentation, 361

sum of rigged orbits, 132

super Jacobi identity, 252

super Leibnitz rule, 251

supercommutative, 251

supercommutator, 248, 252

supergroup, 194

support of a function, 236

symmetric, 344

symmetric algebra, 352

symmetric coordinate system, 279

symmetrization map, 35, 287

symplectic leaf, 264

symplectic reduction, 198, 266

symplectic vector field, 256

symplectomorphism, 256

tame, 354, 392

tangent space, 240

tangent vector, 240

tensor density of the first kind, 245

tensor density of the second kind, 245

tensor field of type (k, l), 244

topological space, 207

topology

uniform, 358

weak, strong, 358

trace, 342

trace class, 342

trace norm, 341

transition functions, 231

transitive action, 321

trivial deformation, 292

twisted product, 239

type I, 354

unimodular coordinate system, 250

unipotent, 112

unipotent radical, 156

unirrep, 73

unit morphism, 212

unitary, 340

unitary dual, 78

unitary representation

of a Lie group, 360

universal enveloping algebra, 286

universal property of coadjoint orbits, 17

vacuum vector, 45

vector bundle, 239

natural, 243

vector differential form, 251

vector field, 240

vector product of quaternions, 273

velocity, 240

Virasoro-Bott group, 22

virtual coadjoint orbit, 122

von Neumann algebra, 352

decomposable, 352

weak integral, 336

weakly containment, 106

weight, 246

weight lattice, 307

weight vector, 245

Weyl algebra, 40

Weyl chamber, 300

open, 300

positive, 300

Weyl group, 154, 299, 324

wild, 354

Witt theorem, 28