On the Triple Product Formula: Real Local Calculations

2017 ◽  
pp. 275-298
Author(s):  
Michael Woodbury
Keyword(s):  
Product Formula ◽  
Triple Product

2051. A Geometrical Proof of the Vector Triple Product Formula

1949 ◽  
Vol 33 (304) ◽  
pp. 126
Author(s):  
G. J. Whitrow
Keyword(s):  
Product Formula ◽  
Triple Product ◽  
Geometrical Proof

2176. On the Vector Triple Product Formula

1950 ◽  
Vol 34 (310) ◽  
pp. 295
Author(s):  
G. J. Whitrow
Keyword(s):  
Product Formula ◽  
Triple Product

Remarks on the rightmost critical value of the triple product L-function

2021 ◽  
pp. 1-16
Author(s):  
Kengo Fukunaga ◽  
Kohta Gejima
Keyword(s):  
Critical Value ◽  
Product Formula ◽  
Orthogonal Basis ◽  
Triple Product ◽  
Explicit Formulas ◽  
Arithmetic Expression ◽  
Weighted Averages ◽  
Hecke Eigenforms ◽  
Hecke Eigenform ◽  
The Individual

Let [Formula: see text] be a normalized cuspidal Hecke eigenform. We give explicit formulas for weighted averages of the rightmost critical values of triple product [Formula: see text]-functions [Formula: see text], where [Formula: see text] and [Formula: see text] run over an orthogonal basis of [Formula: see text] consisting of normalized cuspidal Hecke eigenforms. Those explicit formulas provide us an arithmetic expression of the rightmost critical value of the individual triple product [Formula: see text]-functions.

scholarly journals Poles of triple product L-functions involving monomial representations

2021 ◽  
pp. 1-8
Author(s):  
Heekyoung Hahn
Keyword(s):  
Tensor Product ◽  
Product Formula ◽  
Triple Product ◽  
Natural Setting ◽  
Automorphic Representations ◽  
Cuspidal Automorphic Representations ◽  
Beyond Endoscopy ◽  
Monomial Representations ◽  
Point Of Reference

In this paper, we study the order of the pole of the triple tensor product [Formula: see text]-functions [Formula: see text] for cuspidal automorphic representations [Formula: see text] of [Formula: see text] in the setting where one of the [Formula: see text] is a monomial representation. In the view of Brauer theory, this is a natural setting to consider. The results provided in this paper give crucial examples that can be used as a point of reference for Langlands’ beyond endoscopy proposal.

scholarly journals A triple product formula for plane partitions derived from biorthogonal polynomials

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Shuhei Kamioka
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Laguerre Polynomials ◽  
Product Formula ◽  
Triple Product ◽  
Lattice Paths ◽  
Plane Partitions ◽  
International Audience ◽  
Biorthogonal Polynomials ◽  
Bounded Size

International audience A new triple product formulae for plane partitions with bounded size of parts is derived from a combinato- rial interpretation of biorthogonal polynomials in terms of lattice paths. Biorthogonal polynomials which generalize the little q-Laguerre polynomials are introduced to derive a new triple product formula which recovers the classical generating function in a triple product by MacMahon and generalizes the trace-type generating functions in double products by Stanley and Gansner.

An Alternate Proof of the Vector Triple Product Formula

1986 ◽  
Vol 17 (1) ◽  
pp. 73
Author(s):  
William C. Schulz
Keyword(s):  
Product Formula ◽  
Triple Product ◽  
Alternate Proof

On the universal envelope of a Jordan triple system of n × n matrices

2021 ◽  
pp. 2250126
Author(s):  
Hader A. Elgendy
Keyword(s):  
Triple System ◽  
Product Formula ◽  
Triple Product ◽  
Irreducible Representations ◽  
Monomial Basis ◽  
Jordan Triple System ◽  
Finite Dimensional

We study the universal (associative) envelope of the Jordan triple system of all [Formula: see text] [Formula: see text] matrices with the triple product [Formula: see text] over a field of characteristic 0. We use the theory of non-commutative Gröbner–Shirshov bases to obtain the monomial basis and the center of the universal envelope. We also determine the decomposition of the universal envelope and show that there exist only five finite-dimensional inequivalent irreducible representations of the Jordan triple system of all [Formula: see text] matrices.

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