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.










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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















up vote
18
down vote

favorite
3












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.










share|cite|improve this question




















  • 2




    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













up vote
18
down vote

favorite
3









up vote
18
down vote

favorite
3






3





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.










share|cite|improve this question















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






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edited Nov 14 at 12:13









user21820

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721615










asked Nov 14 at 2:54









Ben Webster

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  • 2




    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














  • 2




    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








2




2




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










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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.






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    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.






    share|cite|improve this answer

























      up vote
      13
      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.






      share|cite|improve this answer























        up vote
        13
        down vote










        up vote
        13
        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.






        share|cite|improve this answer












        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.







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        share|cite|improve this answer










        answered Nov 14 at 4:40









        Timothy Chow

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