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visits | member for | 4 years, 10 months |
seen | Dec 17 at 20:26 | |
stats | profile views | 3,086 |
Oct 24 |
comment |
Annihillator of the highest weight vector in a finite-dimensional representation
"Degree" actually means weight. In fact, I want something more general. Let $\lambda$ be any weight. Then we can consider the Verma module $M(\lambda)$ and the simple module $L(\lambda)$. We know exactly for which $\lambda$ these are not isomorphic and in what weights they are different for every $\lambda$ (this is given by the Shapovalov determinant formula). I'd like to see this explicitly - namely, for every such weight I'd like to have an explicit (one) element of $M(\lambda)$ which vanishes in $L(\lambda)$. |
Oct 23 |
comment |
Annihillator of the highest weight vector in a finite-dimensional representation
I am not looking for a general answer, I need just some non-trivial elements. For example, I expect that it should be possible to write one canonical element for every degree. |
Oct 23 |
asked | Annihillator of the highest weight vector in a finite-dimensional representation |
Oct 4 |
comment |
Weight multiplicity formulae for $(\mathfrak g,B)$-irreps
I second what Jim says - I doubt that there is anything better than what is given by the Kazhdan-Lusztig conjecture. |
Aug 18 |
accepted | FIltrations on a vector bundle on a curve |
Aug 18 |
comment |
FIltrations on a vector bundle on a curve
Thanks! This was exactly the reference I was looking for. |
Aug 17 |
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FIltrations on a vector bundle on a curve
No, the point is that if $E$ has rank 2 then the claim is that we can find a line subbundle $E_1$ of $E$ such that $deg(E_1)-deg(E/E_1)$ is not too small (I think you can always make it smaller than $g$ in this case) -- this is true even when the degree of $E$ is very negative. |
Aug 17 |
revised |
FIltrations on a vector bundle on a curve
added 19 characters in body |
Aug 16 |
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FIltrations on a vector bundle on a curve
Yes, if you wish (otherwise the question is empty) |
Aug 16 |
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FIltrations on a vector bundle on a curve
Well, it has something to do with Harder-Narasimhan, but it is not quite that. For example, if $n=2$ then the statement is that any rank 2 bundle has a line sub-bundle whose degree is not too small. |
Aug 16 |
asked | FIltrations on a vector bundle on a curve |
Aug 16 |
accepted | A question on non-archimedian Fourier transform |
Aug 16 |
answered | A question on non-archimedian Fourier transform |
Aug 14 |
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Quasi-affineness of the base of a $\mathbb{G}_a$-torsor
Actually, I suspect that the answer might be yes, if you assume that $Y$ is separated. |
Aug 14 |
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A question on non-archimedian Fourier transform
By nilcone he actually means degenerate matrices, but there is one point in his proof that I don't understand. |
Aug 14 |
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A question on non-archimedian Fourier transform
Actually I don't understand why the center of $Mp(2)$ acts non-trivially in this representation. |
Aug 14 |
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A question on non-archimedian Fourier transform
OK, I agree (about the invariance of the condition - I just made a stupid computational mistake). Well, in this case we seem to have a contradition in mathematics, since I also don't see any flaw in Roman's argument (which shows that such a distribution can't exist...). |
Aug 14 |
comment |
A question on non-archimedian Fourier transform
Actually, I think that the equation $\psi(AXB)=|\det(A)\det(B)|^{-1}\psi(X)$ is not invariant under the Fourier transform. Am I wrong? |
Aug 14 |
comment |
A question on non-archimedian Fourier transform
Below Semyon claims that there is a distribution on degenerate matrices whose FT is concentrated there as well, but so far I don't understand all the details. |
Aug 14 |
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A question on non-archimedian Fourier transform
Yes, sure, I got confused too about something. Semyon, why is this distribution unique? |