Is there an accessible exposition of Gelfand-Tsetlin theory?
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I'm hoping to start an undergraduate on a project that involves understanding a bit of Gelfand-Tsetlin theory, and have been tearing my hair out looking for a good reference for them to look at. Basically what I would want is something at the level of Vershik-Okounkov (or the book based on it) but for finite dimensional representations of $GL_n$. I feel like such a book or at least some expository notes should exist, but I have had zero luck finding any.
reference-request co.combinatorics rt.representation-theory lie-algebras
edited Nov 14 at 12:13
user21820
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asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
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up vote
17
down vote
favorite
I'm hoping to start an undergraduate on a project that involves understanding a bit of Gelfand-Tsetlin theory, and have been tearing my hair out looking for a good reference for them to look at. Basically what I would want is something at the level of Vershik-Okounkov (or the book based on it) but for finite dimensional representations of $GL_n$. I feel like such a book or at least some expository notes should exist, but I have had zero luck finding any.
reference-request co.combinatorics rt.representation-theory lie-algebras
edited Nov 14 at 12:13
user21820
721615
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
1
Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue"
– David White
Nov 14 at 18:00
add a comment |
up vote
17
down vote
favorite
up vote
17
down vote
favorite
I'm hoping to start an undergraduate on a project that involves understanding a bit of Gelfand-Tsetlin theory, and have been tearing my hair out looking for a good reference for them to look at. Basically what I would want is something at the level of Vershik-Okounkov (or the book based on it) but for finite dimensional representations of $GL_n$. I feel like such a book or at least some expository notes should exist, but I have had zero luck finding any.
reference-request co.combinatorics rt.representation-theory lie-algebras
edited Nov 14 at 12:13
user21820
721615
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
I'm hoping to start an undergraduate on a project that involves understanding a bit of Gelfand-Tsetlin theory, and have been tearing my hair out looking for a good reference for them to look at. Basically what I would want is something at the level of Vershik-Okounkov (or the book based on it) but for finite dimensional representations of $GL_n$. I feel like such a book or at least some expository notes should exist, but I have had zero luck finding any.
reference-request co.combinatorics rt.representation-theory lie-algebras
reference-request co.combinatorics rt.representation-theory lie-algebras
edited Nov 14 at 12:13
user21820
721615
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
edited Nov 14 at 12:13
user21820
721615
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
edited Nov 14 at 12:13
user21820
721615
edited Nov 14 at 12:13
user21820
721615
edited Nov 14 at 12:13
user21820
721615
721615
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
asked Nov 14 at 2:54
Ben Webster♦
32.4k992204
32.4k992204
1
Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue"
– David White
Nov 14 at 18:00
add a comment |
1
Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue"
– David White
Nov 14 at 18:00
1
1
Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue"
– David White
Nov 14 at 18:00
Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue"
– David White
Nov 14 at 18:00
add a comment |
1 Answer
1
active
oldest
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up vote
12
down vote
Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper by Hersh and Lenart as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as this paper, might be helpful.
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
12
down vote
Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper by Hersh and Lenart as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as this paper, might be helpful.
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
add a comment |
up vote
12
down vote
Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper by Hersh and Lenart as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as this paper, might be helpful.
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
add a comment |
up vote
12
down vote
up vote
12
down vote
Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper by Hersh and Lenart as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as this paper, might be helpful.
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
Good question. I've found this to be a difficult subject to get into myself. An abstract approach can seem arcane, but concrete constructions can be complicated and messy. You might try the paper by Hersh and Lenart as a starting point. They take a concrete approach, which has the advantage that you can start computing with small examples relatively quickly. A disadvantage is that your student might miss the big picture of how all this fits into the general representation theory of classical Lie algebras. For that, perhaps the work of Molev, such as this paper, might be helpful.
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
answered Nov 14 at 4:40
Timothy Chow
33.9k11177304
33.9k11177304
add a comment |
add a comment |
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Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue"
– David White
Nov 14 at 18:00