unipotent subgroup
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2016 ◽  
Vol 26 (04) ◽  
pp. 789-841 ◽  
Author(s):  
M. A. Pellegrini ◽  
A. E. Zalesski

Let [Formula: see text] be a finite simple group of Lie type. In this paper, we study characters of [Formula: see text] that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of [Formula: see text]. Such characters can be viewed as a natural generalization of the Steinberg character. For groups [Formula: see text] of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.



Author(s):  
Т.А. Осетрова ◽  
Я.Н. Нужин
Keyword(s):  

Описаны подгруппы группы Шевалле ранга 2 над полем, содержащие ее унипотентную подгруппу.



2012 ◽  
Vol 55 (4) ◽  
pp. 673-688 ◽  
Author(s):  
Avraham Aizenbud ◽  
Dmitry Gourevitch

AbstractLet F be a non-Archimedean local field or a finite field. Let n be a natural number and k be 1 or 2. Consider G := GLn+k(F) and let M := GLn(F) × GLk(F) < G be a maximal Levi subgroup. Let U < G be the corresponding unipotent subgroup and let P = MU be the corresponding parabolic subgroup. Let be the Jacquet functor, i.e., the functor of coinvariants with respect toU. In this paper we prove that J is a multiplicity free functor, i.e., dim HomM(J(π), ρ) ≤ 1, for any irreducible representations π of G and ρ of M. We adapt the classical method of Gelfand and Kazhdan, which proves the “multiplicity free” property of certain representations to prove the “multiplicity free” property of certain functors. At the end we discuss whether other Jacquet functors are multiplicity free.





2012 ◽  
Vol 185 (3) ◽  
pp. 448-457
Author(s):  
V. M. Levchuk ◽  
G. S. Suleimanova


2012 ◽  
Vol 256 (2) ◽  
pp. 381-405
Author(s):  
Dmitri Panyushev
Keyword(s):  


2012 ◽  
Vol 136 (2) ◽  
pp. 149-161
Author(s):  
Dmitri I. Panyushev
Keyword(s):  


2012 ◽  
Vol 349 (1) ◽  
pp. 98-116 ◽  
Author(s):  
Vladimir M. Levchuk ◽  
Galina S. Suleimanova


2012 ◽  
Vol 52 (2) ◽  
pp. 277-331 ◽  
Author(s):  
Yoshiyuki Kimura


Author(s):  
Ben Brubaker ◽  
Daniel Bump ◽  
Solomon Friedberg

This chapter describes the properties of Kashiwara's crystal and its role in unipotent p-adic integrations related to Whittaker functions. In many cases, integrations of representation theoretic import over the maximal unipotent subgroup of a p-adic group can be replaced by a sum over Kashiwara's crystal. Partly motivated by the crystal description presented in Chapter 2 of this book, this perspective was advocated by Bump and Nakasuji. Later work by McNamara and Kim and Lee extended this philosophy yet further. Indeed, McNamara shows that the computation of the metaplectic Whittaker function is initially given as a sum over Kashiwara's crystal. The chapter considers Kostant's generating function, the character of the quantized enveloping algebra, and its association with Kashiwara's crystal, along with the Kostant partition function and the Weyl character formula.



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