What is the meaning of $rho nu_{rho}$? The 2019 Stack Overflow Developer Survey Results Are...
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What is the meaning of $rho nu_{rho}$?
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Dimension of Hom(U, V)$p$-adic representation and $p$-adic analytic group ($p$-adic Lie group)How to prove that $zeta*zeta=zeta$?Why $rho(t)^{-1}(H-frac{partial}{partial h_{rho^{vee}}}) rho(t) = H - frac{1}{2}(rho^{vee}, rho^{vee})$?What are the main differences among representations of $GL(n, mathbb{R})$, $GL(n, mathbb{C})$, and $GL(n,k)$?What is the natural map $U_{A} otimes_A mathbb{Q}(q) to U_q$ and what are the elements in $U_{epsilon}$?Composing outer automorphisms with group representationsNotation for the local polynomial of a Weil representationConfusion about this notation for representation families $ R_1 times_{H} R_2$Why does the Frobenius-semisimplicity of a Weil representation not depend on the choice of the Frobenius element?
$begingroup$
I am reading the paper. On page 14, section 3.1, I am trying to understand the notation $rho nu_{rho}$, where $rho$ is a supercuspidal representation $GL_n(F)$, $F$ is a non-archimedean local field with normalized absolute value $|cdot|$, $nu_{rho} = |cdot|^{s_{rho}}$, $s_{rho}$ is some real number. Is $nu_{rho}$ a representation of $GL_n(F)$? Does $rho nu_{rho}$ mean the composition of two representations of $GL_n(F)$? Thank you very much.
number-theory representation-theory p-adic-number-theory
asked Mar 22 at 21:02
LJRLJR
6,66641850
$endgroup$
add a comment |
$begingroup$
I am reading the paper. On page 14, section 3.1, I am trying to understand the notation $rho nu_{rho}$, where $rho$ is a supercuspidal representation $GL_n(F)$, $F$ is a non-archimedean local field with normalized absolute value $|cdot|$, $nu_{rho} = |cdot|^{s_{rho}}$, $s_{rho}$ is some real number. Is $nu_{rho}$ a representation of $GL_n(F)$? Does $rho nu_{rho}$ mean the composition of two representations of $GL_n(F)$? Thank you very much.
number-theory representation-theory p-adic-number-theory
asked Mar 22 at 21:02
LJRLJR
6,66641850
$endgroup$
$begingroup$
With the p.7 it suggests $(pi |.|^s)(a) v = |det(a)|^s pi(a) v$ so for $pi_1,pi_2$ two representations of $GL_n(R)$ and $a,b in GL_n(R)$ let $Pi_s(pmatrix{a & * \ 0 & b}) (v otimes w )= |det(a)|^spi_1(a) v otimes pi_2 (b)w $ then $pi_1 |.|^s times pi_2 = Ind_P^{GL_{n+n}(R)} Pi_s$ where $ P = { pmatrix{a & * \ 0 & b}, a,b in GL_n(R)}$
$endgroup$
– reuns
Mar 23 at 3:20
add a comment |
$begingroup$
I am reading the paper. On page 14, section 3.1, I am trying to understand the notation $rho nu_{rho}$, where $rho$ is a supercuspidal representation $GL_n(F)$, $F$ is a non-archimedean local field with normalized absolute value $|cdot|$, $nu_{rho} = |cdot|^{s_{rho}}$, $s_{rho}$ is some real number. Is $nu_{rho}$ a representation of $GL_n(F)$? Does $rho nu_{rho}$ mean the composition of two representations of $GL_n(F)$? Thank you very much.
number-theory representation-theory p-adic-number-theory
asked Mar 22 at 21:02
LJRLJR
6,66641850
$endgroup$
I am reading the paper. On page 14, section 3.1, I am trying to understand the notation $rho nu_{rho}$, where $rho$ is a supercuspidal representation $GL_n(F)$, $F$ is a non-archimedean local field with normalized absolute value $|cdot|$, $nu_{rho} = |cdot|^{s_{rho}}$, $s_{rho}$ is some real number. Is $nu_{rho}$ a representation of $GL_n(F)$? Does $rho nu_{rho}$ mean the composition of two representations of $GL_n(F)$? Thank you very much.
number-theory representation-theory p-adic-number-theory
number-theory representation-theory p-adic-number-theory
asked Mar 22 at 21:02
LJRLJR
6,66641850
asked Mar 22 at 21:02
LJRLJR
6,66641850
asked Mar 22 at 21:02
LJRLJR
6,66641850
asked Mar 22 at 21:02
LJRLJR
6,66641850
asked Mar 22 at 21:02
LJRLJR
6,66641850
6,66641850
$begingroup$
With the p.7 it suggests $(pi |.|^s)(a) v = |det(a)|^s pi(a) v$ so for $pi_1,pi_2$ two representations of $GL_n(R)$ and $a,b in GL_n(R)$ let $Pi_s(pmatrix{a & * \ 0 & b}) (v otimes w )= |det(a)|^spi_1(a) v otimes pi_2 (b)w $ then $pi_1 |.|^s times pi_2 = Ind_P^{GL_{n+n}(R)} Pi_s$ where $ P = { pmatrix{a & * \ 0 & b}, a,b in GL_n(R)}$
$endgroup$
– reuns
Mar 23 at 3:20
add a comment |
$begingroup$
With the p.7 it suggests $(pi |.|^s)(a) v = |det(a)|^s pi(a) v$ so for $pi_1,pi_2$ two representations of $GL_n(R)$ and $a,b in GL_n(R)$ let $Pi_s(pmatrix{a & * \ 0 & b}) (v otimes w )= |det(a)|^spi_1(a) v otimes pi_2 (b)w $ then $pi_1 |.|^s times pi_2 = Ind_P^{GL_{n+n}(R)} Pi_s$ where $ P = { pmatrix{a & * \ 0 & b}, a,b in GL_n(R)}$
$endgroup$
– reuns
Mar 23 at 3:20
$begingroup$
With the p.7 it suggests $(pi |.|^s)(a) v = |det(a)|^s pi(a) v$ so for $pi_1,pi_2$ two representations of $GL_n(R)$ and $a,b in GL_n(R)$ let $Pi_s(pmatrix{a & * \ 0 & b}) (v otimes w )= |det(a)|^spi_1(a) v otimes pi_2 (b)w $ then $pi_1 |.|^s times pi_2 = Ind_P^{GL_{n+n}(R)} Pi_s$ where $ P = { pmatrix{a & * \ 0 & b}, a,b in GL_n(R)}$
$endgroup$
– reuns
Mar 23 at 3:20
$begingroup$
With the p.7 it suggests $(pi |.|^s)(a) v = |det(a)|^s pi(a) v$ so for $pi_1,pi_2$ two representations of $GL_n(R)$ and $a,b in GL_n(R)$ let $Pi_s(pmatrix{a & * \ 0 & b}) (v otimes w )= |det(a)|^spi_1(a) v otimes pi_2 (b)w $ then $pi_1 |.|^s times pi_2 = Ind_P^{GL_{n+n}(R)} Pi_s$ where $ P = { pmatrix{a & * \ 0 & b}, a,b in GL_n(R)}$
$endgroup$
– reuns
Mar 23 at 3:20
add a comment |
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$begingroup$
With the p.7 it suggests $(pi |.|^s)(a) v = |det(a)|^s pi(a) v$ so for $pi_1,pi_2$ two representations of $GL_n(R)$ and $a,b in GL_n(R)$ let $Pi_s(pmatrix{a & * \ 0 & b}) (v otimes w )= |det(a)|^spi_1(a) v otimes pi_2 (b)w $ then $pi_1 |.|^s times pi_2 = Ind_P^{GL_{n+n}(R)} Pi_s$ where $ P = { pmatrix{a & * \ 0 & b}, a,b in GL_n(R)}$
$endgroup$
– reuns
Mar 23 at 3:20