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Artykuły w czasopismach na temat "Gelfand–Graev representation":
Mishra, Manish, i Basudev Pattanayak. "Principal series component of Gelfand-Graev representation". Proceedings of the American Mathematical Society 149, nr 11 (5.08.2021): 4955–62. http://dx.doi.org/10.1090/proc/15642.
Chan, Kei Yuen, i Gordan Savin. "Iwahori component of the Gelfand–Graev representation". Mathematische Zeitschrift 288, nr 1-2 (23.03.2017): 125–33. http://dx.doi.org/10.1007/s00209-017-1882-3.
Breeding-Allison, Jeffery, i Julianne Rainbolt. "The Gelfand–Graev representation of GSp(4,𝔽q)". Communications in Algebra 47, nr 2 (17.01.2019): 560–84. http://dx.doi.org/10.1080/00927872.2018.1485228.
Rainbolt, Julianne G. "The Gelfand–Graev Representation of U(3,q)". Journal of Algebra 188, nr 2 (luty 1997): 648–85. http://dx.doi.org/10.1006/jabr.1996.6860.
TAYLOR, JAY. "GENERALIZED GELFAND–GRAEV REPRESENTATIONS IN SMALL CHARACTERISTICS". Nagoya Mathematical Journal 224, nr 1 (9.09.2016): 93–167. http://dx.doi.org/10.1017/nmj.2016.33.
Curtis, Charles W., i Ken-ichi Shinoda. "Unitary Kloosterman Sums and the Gelfand–Graev Representation of GL2". Journal of Algebra 216, nr 2 (czerwiec 1999): 431–47. http://dx.doi.org/10.1006/jabr.1998.7807.
Kochubei, Anatoly N., i Yuri Kondratiev. "Representations of the infinite-dimensional p-adic affine group". Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, nr 01 (marzec 2020): 2050002. http://dx.doi.org/10.1142/s0219025720500022.
HIROSHI, ANDO. "ON THE LOCAL STRUCTURE OF THE REPRESENTATION OF A LOCAL GAUGE GROUP". Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, nr 02 (czerwiec 2010): 223–42. http://dx.doi.org/10.1142/s0219025710004036.
Curtis, Charles W. "On the irreducible components of a Gelfand–Graev representation of a finite Chevalley group". Pacific Journal of Mathematics 307, nr 1 (8.08.2020): 109–19. http://dx.doi.org/10.2140/pjm.2020.307.109.
Bonnafé, Cédric, i Raphaël Rouquier. "Coxeter Orbits and Modular Representations". Nagoya Mathematical Journal 183 (2006): 1–34. http://dx.doi.org/10.1017/s0027763000009259.
Rozprawy doktorskie na temat "Gelfand–Graev representation":
Li, Tzu-Jan. "On the endomorphism algebra of Gelfand–Graev representations and the unipotent ℓ-block of p-adic GL2 with ℓ ≠ p". Thesis, Sorbonne université, 2022. http://www.theses.fr/2022SORUS271.
Inspired by the conjecture of local Langlands in families of Dat, Helm, Kurinczuk and Moss, for a connected reductive group G defined over F_q, we study the relations of the following three rings: (i) the Z-model E_G of endomorphism algebras of Gelfand–Graev representations of G(F_q); (ii) the Grothendieck ring K_{G*} of the category of representations of G*(F_q) of finite dimension over F_q, with G* the Deligne–Lusztig dual of G; (iii) the ring of functions B_{G^vee} of (T^vee // W)^{F^vee}, with G^vee the Langlands dual (defined and split over Z) of G. We show that Z[1/pM]E_G simeq Z[1/pM]K_{G*} as Z[1/pM]-algebras with p = char(F_q) and M the product of bad primes for G, and that K_{G*} simeq B_{G^vee} as rings when the derived subgroup of G^vee is simply-connected. Benefiting from these results, we then give an explicit description of the unipotent l-block of p-adic GL_2 with l different from p. The material of this work, except for § 4, mainly originates from my article [Li2] and from my other article [LiSh] in collaboration with J. Shotton
Taylor, Jonathan. "On Unipotent Supports of Reductive Groups With a Disconnected Centre". Phd thesis, University of Aberdeen, 2012. http://tel.archives-ouvertes.fr/tel-00709051.
Let $\mathbf{G}$ be a connected reductive algebraic group defined over an algebraic closure of the finite field of prime order $p>0$, which we assume to be good for $\mathbf{G}$. We denote by $F : \mathbf{G} \to \mathbf{G}$ a Frobenius endomorphism of $\mathbf{G}$ and by $G$ the corresponding $\mathbb{F}_q$-rational structure. If $\operatorname{Irr}(G)$ denotes the set of ordinary irreducible characters of $G$ then by work of Lusztig and Geck we have a well defined map $\Phi_{\mathbf{G}} : \operatorname{Irr}(G) \to \{F\text{-stable unipotent conjugacy classes of }\mathbf{G}\}$ where $\Phi_{\mathbf{G}}(\chi)$ is the unipotent support of $\chi$.
Lusztig has given a classification of the irreducible characters of $G$ and obtained their degrees. In particular he has shown that for each $\chi \in \operatorname{Irr}(G)$ there exists an integer $n_{\chi}$ such that $n_{\chi}\cdot\chi(1)$ is a monic polynomial in $q$. Given a unipotent class $\mathcal{O}$ of $\mathbf{G}$ with representative $u \in \mathbf{G}$ we may define $A_{\mathbf{G}}(u)$ to be the finite quotient group $C_{\mathbf{G}}(u)/C_{\mathbf{G}}(u)^{\circ}$. If the centre $Z(\mathbf{G})$ is connected and $\mathbf{G}/Z(\mathbf{G})$ is simple then Lusztig and H\'zard have independently shown that for each $F$-stable unipotent class $\mathcal$ of $\mathbf$ there exists $\chi \in \operatorname(G)$ such that $\Phi_(\chi)=\mathcal$ and $n_ = |A_(u)|$, (in particular the map $\Phi_$ is surjective).
The main result of this thesis extends this result to the case where $\mathbf$ is any simple algebraic group, (hence removing the assumption that $Z(\mathbf)$ is connected). In particular if $\mathbf$ is simple we show that for each $F$-stable unipotent class $\mathcal$ of $\mathbf$ there exists $\chi \in \operatorname(G)$ such that $\Phi_(\chi) = \mathcal$ and $n_ = |A_(u)^F|$ where $u \in \mathcal^F$ is a well-chosen representative. We then apply this result to prove, (for most simple groups), a conjecture of Kawanaka's on generalised Gelfand--Graev representations (GGGRs). Namely that the GGGRs of $G$ form a $\mathbf{Z}$-basis for the $\mathbf{Z}$-module of all unipotently supported class functions of $G$. Finally we obtain an expression for a certain fourth root of unity associated to GGGRs in the case where $\mathbf{G}$ is a symplectic or special orthogonal group.
Części książek na temat "Gelfand–Graev representation":
Curtis, Charles W. "On the Endomorphism Algebras of Gelfand-Graev Representations". W Finite Dimensional Algebras and Related Topics, 27–35. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-1556-0_2.
Curtis, Charles W., i Toshiaki Shoji. "A Norm Map for Endomorphism Algebras of Gelfand-Graev Representations". W Finite Reductive Groups: Related Structures and Representations, 185–94. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4124-9_7.
"Regular elements; Gelfand-Graev representations". W Representations of Finite Groups of Lie Type, 119–42. Cambridge University Press, 1991. http://dx.doi.org/10.1017/cbo9781139172417.016.
"Regular Elements; Gelfand–Graev Representations; Regular and Semi-Simple Characters". W Representations of Finite Groups of Lie Type, 196–224. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108673655.014.
"Jacquet modules corresponding to Gelfand - Graev characters of parabolically induced representations". W The Descent Map from Automorphic Representations of GL(n) to Classical Groups, 81–120. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814304993_0005.
"Coefficients of Gelfand-Graev Type, of Fourier-Jacobi Type, and Descent". W The Descent Map from Automorphic Representations of GL(n) to Classical Groups, 41–63. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814304993_0003.
Yamashita, Hiroshi. "Multiplicity One Theorems for Generalized Gelfand-Graev Representations of Semisimple Lie Groups and Whittaker Models for the Discrete Series". W Representations of Lie Groups, Kyoto, Hiroshima, 1986, 31–121. Elsevier, 1988. http://dx.doi.org/10.1016/b978-0-12-525100-6.50007-2.