Letellier E. — Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Letellier E. — Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

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Название: Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras

Автор: Letellier E.

Аннотация:

The Fourier transforms of invariant functions on finite reductive Lie algebras are due to T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.

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Рубрика: Математика/Алгебра/Теория представлений/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 155

Добавлена в каталог: 19.03.2005

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Предметный указатель

      6
$a_{\mathcalG}$       85
      6
$D_X\colon\mathcal{D}_c^b(X)\to\mathcal{D}^b_C(X)$       46
$e_\alpha$       11
$f''_\mathcal{O}$       126
      36
      7
$H^1(\theta, H)$       11
      9
$h_\alpha$       11
$j_{s, \mathcal G}$       117
$K(C, \xi)$       54
      58\
      46
$K^X(Y, \varepsilon)$
      121
$K_1^{S\times\mathcal G}$       122
      115
$K_2^{S\times\mathcal G}$       122
$K_{1, \sigma}$       115
$K_{2, \sigma}$       115
      100
$m_\sigma$       90
      6
$P(\varPhi)$       8
$Q(\varPhi)$       8
      7
      7
$R_{L\subset P}^G$       37
$Supp(\mathcal F)$       45
$S_{L\subset P}^G(g, l)$       37
$S_{\mathcal\subset\mathcal P}^{\mathcal G}(x, y)$
      13
      7
      9
      8
$X^U_{\sigma,2, S_{\mathcal{O}},2}$       126
$X_{S,1, o}$       118
$X_{S,1}$       118
$X_{S,2, o}$       118
$X_{S,2, \mathcal{\hat O}}$       124
$X_{S,2}$       118
$X_{S,2}^U$       124
$X_{\sigma,2, S_{\mathcal{O}},2}$       125
$Y^U_{S,2, \mathcal O}$       127
$Y^U_{S,2}$       127
$Y^U_{\sigma, S_{\mathcal O},2}$       1277
      119
$Y_{S,2}$       119
$Y_{\sigma, S_{\mathcal O},2}$       125
$z(\mathcal H)$       5
$z(\mathcal L)_{reg}$       66
      5
$\eta_0^H$       33
$\gamma_S$       119
$\mathbb F_q$ -rank      11
$\mathbf X_{K, \phi}(x)$       58
$\mathcak M_G(\mathcal G)$       53
$\mathcal A_w$
$\mathcal A_{\mathcalG}$       85
$\mathcal D_c^b$       46
$\mathcal F^{\mathcal H}\colon \mathcal C(\mathcal H^F)\to\mathcal C(\mathcal H^F)$       35
$\mathcal F^{\mathcal H}\colon \mathcal D_c^b(\mathcal H^F)\to\mathcal D_c^b(\mathcal H^F)$       90
$\mathcal G'$       7
$\mathcal G_\alpha$       8
$\mathcal L_\varPsi$       84
$\mathcal O_x^G$       6
$\mathcal Q_{\mathcal L, C, \zeta, \phi}^{\mathcal G}(u, v)$       106
$\mathcal Q_{\mathcal L\subset\mathcal P}^{\mathcal G}(u, v)$       38
$\mathcal R_{S\times \mathcal L}^{S\times\mathcal G}$       137
$\mathcal R_{\mathcal L\subset\mathcal P}^{\mathcal G}$       39

$\mathcal U_P$       7
$\mathcal W_G(\varepsilon)$       96
$\mathcal X_\imath$       60
$\mathcal Y_\imath$       59
$\mathrm{ind}_{S\times\mathcal L, \mathcal P}^{S\times\mathcal G}$       115
$\mathrm{ind}_{\mathcal L\subset\mathcal P}^{\mathcal G}$       63
$\mathrm{ind}_{\mathcal Z\times C}^{S\times\mathcal G}$       120
$\mathrm{ind}_{\varSigma}^{\mathcal G}$       76
$\mu$       35
$\mu_{\mathcal H}$       89
$\omega$       38
$\overline G$       7
$\overline{T}$       13
$\overline{\mathcal G}$       7
$\pi_P$       7
$\pi_{\mathcal P}$       7
$\theta_w$       97
$\tilde f_{\mathcal O}$       126
$\tilde\gamma$       145
$\varepsilon_{1, \sigma}$       115
$\varepsilon_{2, \sigma}$       115
$\varPhi=\varPhi(T)$       8
$\varPi$       9
$\varPsi\colon\mathbb F_q^+\to\overline{\mathbb Q}_\ell^\times$       35
$\xi_x^H$       33
Acceptable primes      62
Adjoint      8
Admissible complex      85
Almost-direct product      7
Character sheaf      85
Characteristic function of an -orbit      33
Characteristic function of an F-equivariant complex      58
Chevalley basis      12
COMPLEX      46
Conjugate (K-conjugate)      6 72
Cuspidal admissible complex      84
Cuspidal datum      85
Cuspidal orbital pair      86
Cuspidal orbital perverse sheaf      86
Deligne — Fourier transforms      90
Deligne — Lusztig induction      39
Fourier transforms      35
Generalized Green function      106
Good primes      19
Green function (two-variable...)      37 38
Harish — Chandra induction      34
Highest root      9
Isogeny      8
Lang map      36
Levi subgroup of G      7
Local system      45
Lusztig complex      86
Lusztig constant      145
Modified Lusztig constant      145
Nilpotent complex      87
Nilpotent pair      54
Orbit (K-orbit of $\mathcal H$ )      6
Orbital pair      54
Orbital perverse sheaf      54
Perverse extension      47
Regular (L-regular)      28
Semi-simple $\mathbb F_q$ -rank      11
Semi-simple algebraic group      7
Semi-simple rank      7
Simple components of G      7
Simply connected      8
Split      11
Torsion prime      19
Unipotent complex      87
Unipotent pair      54
Very good primes      19
Weyl group      9

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