On Twisted Orbital Integral Identities for PGL(3) Over A p-adic Field

1990 ◽  
Vol 42 (6) ◽  
pp. 1098-1130 ◽  
Author(s):  
David Joyner
Keyword(s):  
Trace Formula ◽  
Hecke Algebras ◽  
Unit Element ◽  
The Other ◽  
Original Material ◽  
Counting Problems ◽  
Orbital Integral ◽  
Symmetric Square ◽  
Integral Identities

AbstractThe object of this paper is to prove certain p-adic orbital integral identities needed in order to accomplish the symmetric square transfer via the twisted Arthur trace formula. Only §5 of this article contains original material, the rest of it is due to R. Langlands. Very briefly, we reduce the problem of proving certain orbital integral identities for “matching” functions in the respective Hecke algebras to two counting problems on the buildings. We give Langlands’ solution of one of these problems in the case of the unit elements of the respective Hecke algebras and §5 provides the solution to the other one, again, in the unit element case. The main results assume p ≠ 2.

scholarly journals Ukrainian Topics in Slovak Periodicals at Turn of the 20th Century

2019 ◽  
pp. 74-80
Author(s):  
Andrea Draganová ◽  
Luybica Babotova
Keyword(s):  
Statistical Data ◽  
Social Issues ◽  
Relevant Information ◽  
The Other ◽  
Political Activity ◽  
Original Material ◽  
Review Journal ◽  
Conservative Policy ◽  
National Life ◽  
Personal Interests

The article focuses on the representation of Ukrainian topics in Slovak journals, mainly in “Hlas” (‘Voice’). This periodical had a subtitle “Mesačník pre literatúru, politika a sociálne otázky” (Monthly on literature, politics and social issues) and appeared in 1898–1904.  “Hlas” is considered to be the publishing platform of liberally oriented Slovak youth, who opposed the conservative policy of the Center of National Life in Martin, led by S. H. Vajanský. Just as with other key ideological issues (Czechoslovakism, Russophilism, political activity), Vajanský’s reception and understanding of Ukrainian issues significantly differed from those of the younger generation. ‘Ukrainian theme’ usually got into the journal “Hlas” indirectly, through the links to ‘Slovanský přehled’ (‘Slavic Review’) journal. “Hlas” paid considerable attention to social problems. Such issues as migration, the influence of magyarization on the educational system and level of literacy among ‘rusyns’ were often addressed with a help of statistical data. The periodical provided information on the current challenges of Ukrainian students and some translations of works by Ukrainian authors. For instance, in 1903 “Hlas”  published “Nastia” by B. Lepkyi. The translator of the text F. Votruba was among the most active promotors of Ukrainian literature. The references to outstanding Ukrainian cultural figures, such as Taras Shevchenko, Ivan Franko, Volodymyr Hnatiuk, etc., are also worth to mention. A detailed analysis of the content of “Hlas” revealed that the journal gave a low priority to ‘Ukrainian issues’. Most of the relevant information was taken from the other journals. The appearance of original material or translations to a large extent was driven by the personal interests of individual authors.

On the Fundamental Lemma for Standard Endoscopy: Reduction to Unit Elements

1995 ◽  
Vol 47 (5) ◽  
pp. 974-994 ◽  
Author(s):  
Thomas C. Hales
Keyword(s):  
Trace Formula ◽  
Simple Form ◽  
Hecke Algebras ◽  
Orbital Integrals ◽  
Fundamental Lemma ◽  
Stable Trace Formula

AbstractThe fundamental lemma for standard endoscopy follows from the matching of unit elements in Hecke algebras. A simple form of the stable trace formula, based on the matching of unit elements, shows the fundamental lemma to be equivalent to a collection of character identities. These character identities are established by comparing them to a compact-character expansion of orbital integrals.

ON THE QUANTUM RUIJSENAARS MODEL, SOME QUANTUM HOMOGENEOUS SPACES AND HECKE ALGEBRAS

2004 ◽  
Vol 19 (supp02) ◽  
pp. 224-239
Author(s):  
N. IORGOV
Keyword(s):  
Homogeneous Space ◽  
Explicit Form ◽  
Homogeneous Spaces ◽  
Hecke Algebras ◽  
The Other ◽  
Difference Operators ◽  
Quantum Homogeneous Spaces ◽  
Quantum Analogue ◽  
Affine Hecke Algebras

The aim of the article is to derive in the explicit form the radial components of Casimir elements of Uq( gl n) corresponding to a quantum analogue of the homogeneous space GL (n)/ SO (n). They coincide with the Macdonald–Ruijsenaars difference operators (MRDOs), if one starts from a special set of Casimir elements from the center of Uq( gl n). The derivation is essentially based on Cherednik's approach to MRDOs by means of affine Hecke algebras. From the other side, MRDOs coincide with commuting Hamiltonians of quantum trigonometric n-particle Ruijsenaars model.

scholarly journals On the Dimension of Modules and Algebras, IV: Dimension of Residue Rings of Hereditary Rings

1956 ◽  
Vol 10 ◽  
pp. 87-95 ◽  
Author(s):  
Samuel Eilenberg ◽  
Hirosi Nagao ◽  
Tadasi Nakayama
Keyword(s):  
Left Ideal ◽  
Jacobson Radical ◽  
Unit Element ◽  
The Other ◽  
Dedekind Ring ◽  
Integral Domains ◽  
Hereditary Ring ◽  
Common Value ◽  
Residue Ring ◽  
The Common

A ring (with unit element) Λ is called semi-primary if it contains a nilpotent two-sided ideal N such that the residue ring Γ = Λ/N is semi-simple (i.e. l.gl.dim Γ = r.gl.dim Γ = 0). N is then the (Jacobson) radical of Λ. Auslander [1] has shown that if Λ is semi-primary thenThe common value is denoted by gl. dim Λ. On the other hand, for any ring Λ the following conditions are equivalent : (a) 1. gl. dim Λ ≦ 1, (b) each left ideal in Λ is projective, (c) every submodule of a projective left Λ-module is projective. Rings satisfying conditions (a)-(c) are called hereditary. For integral domains the notions of “hereditary ring” and “Dedekind ring” coincide.

scholarly journals BEYOND ENDOSCOPY FOR THE RELATIVE TRACE FORMULA II: GLOBAL THEORY

2017 ◽  
Vol 18 (2) ◽  
pp. 347-447 ◽  
Author(s):  
Yiannis Sakellaridis
Keyword(s):  
Trace Formula ◽  
The Other ◽  
Test Functions ◽  
Trace Formulas ◽  
Global Theory ◽  
Relative Trace Formula ◽  
Kuznetsov Trace Formula ◽  
The One ◽  
Beyond Endoscopy

For the group $G=\operatorname{PGL}_{2}$ we perform a comparison between two relative trace formulas: on the one hand, the relative trace formula of Jacquet for the quotient $T\backslash G/T$, where $T$ is a nontrivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to nonstandard test functions. This gives a new proof of the celebrated result of Waldspurger on toric periods, and suggests a new way of comparing trace formulas, with some analogies to Langlands’ ‘Beyond Endoscopy’ program.

scholarly journals IWASAWA THEORY FOR THE SYMMETRIC SQUARE OF A CM MODULAR FORM AT INERT PRIMES

2011 ◽  
Vol 54 (2) ◽  
pp. 241-259
Author(s):  
ANTONIO LEI
Keyword(s):  
Modular Form ◽  
Complex Multiplication ◽  
Iwasawa Theory ◽  
The Other ◽  
Selmer Groups ◽  
Supersingular Primes ◽  
Supersingular Prime ◽  
Symmetric Square ◽  
The One ◽  
Invent Math

AbstractLet f be a modular form with complex multiplication (CM) and p an odd prime that is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by Delbourgo and Dabrowski (A. Dabrowski and D. Delbourgo, S-adic L-functions attached to the symmetric square of a newform, Proc. Lond. Math. Soc. 74(3) (1997), 559–611), whereas the other one has a similar interpolating properties but corresponds to a different eigenvalue of the Frobenius. The symmetry between these two p-adic L-functions allows us to define the plus and minus p-adic L-functions à la Pollack (R. Pollack, on the p-adic L-function of a modular form at a supersingular prime, Duke Math. J. 118(3) (2003), 523–558). We also define the plus and minus p-Selmer groups analogous to the ones defined by Kobayashi (S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152(1) (2003), 1–36). We explain how to relate these two sets of objects via a main conjecture.

scholarly journals The Selberg trace formula as a Dirichlet series

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Andrew R. Booker ◽  
Min Lee
Keyword(s):  
Dirichlet Series ◽  
Trace Formula ◽  
Weighted Sum ◽  
Selberg Trace Formula ◽  
Quadratic Twists ◽  
Symmetric Square

AbstractWe explore an idea of Conrey and Li of expressing the Selberg trace formula as a Dirichlet series. We describe two applications, including an interpretation of the Selberg eigenvalue conjecture in terms of quadratic twists of certain Dirichlet series, and a formula for an arithmetically weighted sum of the complete symmetric square

scholarly journals Commentary - Methods to find all the edges on any of the shortest paths between two given nodes of a directed acyclic graph

2021 ◽  
Vol 7 ◽  
Author(s):  
Deepak Ahire ◽  
Omkar Jadhav
Keyword(s):  
Dynamic Programming ◽  
Graph Theory ◽  
Directed Acyclic Graph ◽  
Shortest Paths ◽  
The Other ◽  
Use Case ◽  
Counting Problems ◽  
Acyclic Graph ◽  
Questions And Answers ◽  
Community Portal

This article puts forth all the existing methods proposed by the various authors of the Stack Exchange community to find all the edges on any shortest path between two given nodes of a directed acyclic graph. For a directed acyclic graph with N number of nodes, an exponential number of paths are possible between any two given nodes and, thus, it is not feasible to compute every path and find the shortest ones in polynomial time to generate a set of all edges that contribute or make any of the shortest paths. The methods discussed in this article are not limited only to this specific use case, but have a much broader scope in graph theory, dynamic programming and counting problems. Generally, various other questions and answers, raised on the community portal having similar scope to those that the users specifically seek, do not receive sufficient hits and, hence, enough attention and votes for various reasons worth contemplating. Therefore, this article also aims to highlight the various scopes of the methods discussed in this article and acknowledge the efforts of the authors, moderators and contributors of the Stack Exchange community for their expertise and time to write precise answers and share their opinions and advice. Finally, it also appeals to all the other beneficiaries in the community to use their privileges responsibly and upvote the posted answers, if they helped solve their queries, as one upvote is free of cost.

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