Branching Laws and Banking Offices: Comment

1979 ◽  
Vol 11 (2) ◽  
pp. 227 ◽  
Author(s):  
Donald T. Savage ◽  
David Burras Humphrey
Keyword(s):  
Branching Laws

scholarly journals Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kei Yuen Chan
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Branching Laws ◽  
General Linear Groups ◽  
Branching Law

Abstract We prove a local Gan–Gross–Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier–Jacobi models and study a possible generalization to Ext-branching laws.

scholarly journals SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS

2018 ◽  
Vol 19 (5) ◽  
pp. 1521-1572
Author(s):  
Haruzo Hida ◽  
Jacques Tilouine
Keyword(s):  
Power Series ◽  
Galois Representation ◽  
Symmetric Power ◽  
Selmer Groups ◽  
Abelian Surfaces ◽  
Symmetric Powers ◽  
Branching Laws ◽  
Hida Family

We prove, under some assumptions, a Greenberg type equality relating the characteristic power series of the Selmer groups over $\mathbb{Q}$ of higher symmetric powers of the Galois representation associated to a Hida family and congruence ideals associated to (different) higher symmetric powers of that Hida family. We use $R=T$ theorems and a sort of induction based on branching laws for adjoint representations. This method also applies to other Langlands transfers, like the transfer from $\text{GSp}(4)$ to $U(4)$. In that case we obtain a corollary for abelian surfaces.

Branching Laws

2009 ◽  
pp. 363-385 ◽  
Author(s):  
Roe Goodman ◽  
Nolan R. Wallach
Keyword(s):  
Branching Laws

scholarly journals Endoscopie et conjecture locale raffinée de Gan–Gross–Prasad pour les groupes unitaires

2015 ◽  
Vol 151 (7) ◽  
pp. 1309-1371 ◽  
Author(s):  
R. Beuzart-Plessis
Keyword(s):  
Unitary Groups ◽  
Branching Laws ◽  
Epsilon Factors

Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan–Gross–Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors.

scholarly journals Analysis on the minimal representation of O(p,q) II. Branching laws

2003 ◽  
Vol 180 (2) ◽  
pp. 513-550 ◽  
Author(s):  
Toshiyuki Kobayashi ◽  
Bent Ørsted
Keyword(s):  
Minimal Representation ◽  
Branching Laws

scholarly journals Branching laws for small unitary representations of GL(n, ℂ)

2014 ◽  
Vol 25 (06) ◽  
pp. 1450052
Author(s):  
Jan Möllers ◽  
Benjamin Schwarz
Keyword(s):  
Parabolic Subgroup ◽  
Principal Series ◽  
Unitary Representations ◽  
Symmetric Pair ◽  
Maximal Parabolic Subgroup ◽  
Infinite Dimensional ◽  
Branching Laws ◽  
Series Representations ◽  
Unitary Principal Series ◽  
Kirillov Dimension

The unitary principal series representations of G = GL (n, ℂ) induced from a character of the maximal parabolic subgroup P = ( GL (1, ℂ) × GL (n - 1, ℂ)) ⋉ ℂn-1 attain the minimal Gelfand–Kirillov dimension among all infinite-dimensional unitary representations of G. We find the explicit branching laws for the restriction of these representations to all reductive subgroups H of G such that (G, H) forms a symmetric pair.

The stable pedigrees of critical branching populations

1984 ◽  
Vol 21 (3) ◽  
pp. 447-463 ◽  
Author(s):  
Olle Nerman
Keyword(s):  
Limit Theorems ◽  
Branching Processes ◽  
Branching Laws ◽  
Conditional Limit Theorems ◽  
First Results ◽  
Conditional Limit

The asymptotic sizes and compositions of critical general branching processes conditioned on non-extinction are treated. First, results are given for processes counted with random characteristics allowed to depend on the whole daughter processes, then these are used to derive conditional limit theorems for the pedigrees of randomly sampled individuals among populations counted with 0–1-valued characteristics. The limiting stable pedigrees have nice independence structures and are easily derived from the original branching laws.

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