Representations and subgroups of the translation group [closed]
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Let $H_lambda=lambdamathbb{Z}$ for $lambdain mathbb{R}$ be a subgroup of the 1-dimensional translation group $T$. Consider then the factor group $K_{lambda}=T/H_{lambda}$ with representation $U_{lambda}(x)$ for $xin K_{lambda}$. Then are the following two points correct:
1) $exists$ a mapping $x'in T rightarrow x=x'H_lambda in K_lambda$, which is in general many-to-one. $U_lambda$ is also a representation of $T$ but a degenerate one.
2) Can $lambda$ be interpreted as the wavelength of a wave and $U_{lambda}(x)=e^{-ifrac{2pi}{lambda} x}$?
group-theory representation-theory abelian-groups
asked Dec 29 '18 at 3:47
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393
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closed as unclear what you're asking by Cesareo, Lord Shark the Unknown, user91500, Holo, Lee David Chung Lin Dec 30 '18 at 7:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
Let $H_lambda=lambdamathbb{Z}$ for $lambdain mathbb{R}$ be a subgroup of the 1-dimensional translation group $T$. Consider then the factor group $K_{lambda}=T/H_{lambda}$ with representation $U_{lambda}(x)$ for $xin K_{lambda}$. Then are the following two points correct:
1) $exists$ a mapping $x'in T rightarrow x=x'H_lambda in K_lambda$, which is in general many-to-one. $U_lambda$ is also a representation of $T$ but a degenerate one.
2) Can $lambda$ be interpreted as the wavelength of a wave and $U_{lambda}(x)=e^{-ifrac{2pi}{lambda} x}$?
group-theory representation-theory abelian-groups
asked Dec 29 '18 at 3:47
playplay
393
$endgroup$
closed as unclear what you're asking by Cesareo, Lord Shark the Unknown, user91500, Holo, Lee David Chung Lin Dec 30 '18 at 7:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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Is it better now?
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– play
Jan 1 at 3:35
add a comment |
$begingroup$
Let $H_lambda=lambdamathbb{Z}$ for $lambdain mathbb{R}$ be a subgroup of the 1-dimensional translation group $T$. Consider then the factor group $K_{lambda}=T/H_{lambda}$ with representation $U_{lambda}(x)$ for $xin K_{lambda}$. Then are the following two points correct:
1) $exists$ a mapping $x'in T rightarrow x=x'H_lambda in K_lambda$, which is in general many-to-one. $U_lambda$ is also a representation of $T$ but a degenerate one.
2) Can $lambda$ be interpreted as the wavelength of a wave and $U_{lambda}(x)=e^{-ifrac{2pi}{lambda} x}$?
group-theory representation-theory abelian-groups
asked Dec 29 '18 at 3:47
playplay
393
$endgroup$
Let $H_lambda=lambdamathbb{Z}$ for $lambdain mathbb{R}$ be a subgroup of the 1-dimensional translation group $T$. Consider then the factor group $K_{lambda}=T/H_{lambda}$ with representation $U_{lambda}(x)$ for $xin K_{lambda}$. Then are the following two points correct:
1) $exists$ a mapping $x'in T rightarrow x=x'H_lambda in K_lambda$, which is in general many-to-one. $U_lambda$ is also a representation of $T$ but a degenerate one.
2) Can $lambda$ be interpreted as the wavelength of a wave and $U_{lambda}(x)=e^{-ifrac{2pi}{lambda} x}$?
group-theory representation-theory abelian-groups
group-theory representation-theory abelian-groups
asked Dec 29 '18 at 3:47
playplay
393
asked Dec 29 '18 at 3:47
playplay
393
edited Dec 31 '18 at 23:43
play
asked Dec 29 '18 at 3:47
playplay
393
asked Dec 29 '18 at 3:47
playplay
393
asked Dec 29 '18 at 3:47
playplay
393
393
closed as unclear what you're asking by Cesareo, Lord Shark the Unknown, user91500, Holo, Lee David Chung Lin Dec 30 '18 at 7:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Cesareo, Lord Shark the Unknown, user91500, Holo, Lee David Chung Lin Dec 30 '18 at 7:58
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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Is it better now?
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– play
Jan 1 at 3:35
add a comment |
$begingroup$
Is it better now?
$endgroup$
– play
Jan 1 at 3:35
$begingroup$
Is it better now?
$endgroup$
– play
Jan 1 at 3:35
$begingroup$
Is it better now?
$endgroup$
– play
Jan 1 at 3:35
add a comment |
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$begingroup$
Is it better now?
$endgroup$
– play
Jan 1 at 3:35