Index
admissible array, 215
admissible series, 164
algebra
extended reflection equation, 87
Hopf, 9
Mickelsson, 323
Mickelsson-Zhelobenko, 324
Olshanski, 280, 301
quantized enveloping, 36
quantized Kac-Moody, xi
quantum affine, 38, 39
quantum loop, 38
reflection equation, 86
twisted quantized enveloping, 87
antipode, 9
basis
Gelfand-Tsetlin, 193, 197
Young, 223
Bethe ansatz, xvii
betweenness conditions, 192, 352, 354, 355
bialgebra, 9
binary property, 234
Boolean poset, 87
Bruhat order, 87
category Q, 285, 304
cell
addable, 223
removable, 223
centralizer construction, xv
coalgebra, 9
coassociativity, 9
column order, 318
comatrix
quantum, 20
Sklyanin, 63
comultiplication, 9
content, 223
counit, 9
crossing subsets, 222
determinant
Capelli, xiii, 240
Capelli-type, 242
quantum, 13, 187
Sklyanin, 53
virtual, 289, 308
virtual quantum, 281
diagram, 223, 378
skew, 236
Drinfeld functor, xvii
Drinfeld presentation, xiv
Drinfeldian, 43
equation
reflection, 86
Yang-Baxter, 4
extremal projector, 324
function
double Schur, 317
shifted Schur, 284
fusion procedure, 227
Gauss decomposition, 31
Gelfand invariant, xiii, 240, 243
Gelfand-Tsetlin character, 298
Gelfand-Tsetlin subspace, 298
general position, 115
generality condition, 191
group
braid, 37
quantum, xi
Hafnian, 264
Harish-Chandra isomorphism, 239, 242
homomorphism
evaluation, 2, 39, 47
Harish-Chandra, 239, 242
identity
Capelli, xiii
characteristic, 245, 246
higher Capelli, 257
immanant
quantum, 256
virtual quantum, 284
399
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