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Haran S.M.J. — Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations
Haran S.M.J. — Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations

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Название: Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations

Автор: Haran S.M.J.

Аннотация:

In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 217

Добавлена в каталог: 10.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\beta$-highest weight representation      187
$\beta$-highest weight vector      187
$\beta$-integral      27
$\beta$-measure      28
$\gamma$-chain      40
$\gamma$-integral, $\eta-$      25
$\gamma$-integral, complex      52
$\gamma$-integral, p-      24
$\gamma$-measure      25
$\lambda$-highest weight      179
*-homomorphism      191
*-Hopf algebra      192
*-structure      185
Adele ring      125
Adjoint operator      43
Annihilator operator      72
Anti-cohomomorphism      192
Anti-homomorphism      192
Antipode      192
Askey — Wilson operator      201
Askey — Wilson polynomial      184
Basic basis      111
Bessel function      107
Bialgebra      191
Big q-Jacobi polynomial      184
Binomial coefficient      153
Boundary      34
Braid relation      196
Cauchy sequence      45
Cellular basis      170
Clebsch — Gordan coefficients      195
Co-convolution      109
Coassociativity      191
Comodule      179
Comultiplication      191
Convolution      109 138
cos-embedding      163
Counit      191
Counting measure      169
Creation operator      72
Critical angle      144
Cyclic vector      98
Dual measure      102
Extream      43
Flip      192 196
For,Dheis      115
Fourier transform      99
Fourier — Bessel transform      96
Geometric basis      169
Global absolute value      125
Global Fourier — Bessel transform      126
Global semi-group      127
Global zeta function      126
Grassmann manifold      144
Green kernel      44
Haar measure on $\mathbb{Q}*_p$      24
Haar measure on $\mathbb{Q}_p$      24
Hall polynomial      164
Harmonic      43
Harmonic measure      35 46
Harmonic Selberg measure      168
Heisenberg relation      72
Higher rank $\beta$-measure      151
Higher rank beta function      156 173
Higher rank Laguerre measure      154
Higher rank Laguerre polynomial      154
Higher rank Little q-Jacobi polynomials      177
Higher rank multi-variable Jacobi polynomial      154
Highest weight vector      193
Hopf algebra      190
Idele group      125
Idempotent      139
Immanent      177
Infinitesimal generator      102 118
Jackson q-gamma function      54
Jacobi matrix      119
Kernel      106
Koornwinder operator      184
Koornwinder polynomial      184
Koornwinder weight      184
Little q-Jacobi polynomial      184
Littlewood — Richardson coefficient      182
Littlewood — Richardson coefficients      164
Markov chain      35 42
Martin kernel      44
Martin metric      45
Meixner — Pollaczeck polynomial      121
Mellin transform      99
Monomial symmetric function      156
Multi-variable Jacobi polynomial      156
Multi-variable Laguerre polynomial      156
Multiplication      192
Non-symmetric $\beta$-chain      37
p-adic substitution      55
p-Hahn basis      40
p-Jacobi basis      40
p-Laguerre basis      41
Partition      160
Polynomial, little q-Jacobi      76
Pure basis      121
q-$\beta$-chain      55
q-$\beta$-measure      60
q-$\gamma$-chain      77
q-binomial coefficient      56
q-binomial theorem      56
q-factorial      56
q-Fourier transform      107
q-Hahn polynomial      79
q-Heisenberg algebra      114
q-Laguerre polynomial      79
q-Mellin transform      104
q-number      56
q-Selberg measure      173
q-Tate measure      103
q-zeta function      54
Quantum Grassmann manifolds      182
Quantum groups      185
Quantum Yang — Baxter equation      196
Random walk      37
Real $\beta$-chain      47
Real substitution      55
Reflection equation      183
Riemann hypothesis      129
Root      34
Rosetta stone      1
Schubert cell      200
Schur function      180
Schur’s lemma      139
Semi-group      123
Shifted Macdonald polynomial      177
sin-embedding      163
State space      35 42
Super harmonic      45
Symmetric $\beta$-chain      36
Tableau      164
Tate measure      95 100
Tate thesis      100
Transition probability      35 42
TREE      20 34
TYPE      144
UNIT      192
Unitary      180
Universal enveloping algebra      181
Universal R-matrix      178 196
VACUUM      72
Vandermonde determinant      173
Weight      193
Zonal spherical functions      137
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