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Sep
26
awarded  Good Answer
Sep
26
revised How to prove this polynomial always has integer values at all integers?
formula ran off page
Sep
26
revised How to prove this polynomial always has integer values at all integers?
formula ran off page
Sep
26
awarded  Enlightened
Sep
25
comment How to prove this polynomial always has integer values at all integers?
It was take home.
Sep
23
comment cohomology theory for algebraic groups
@David_Stuart The paper by Brian is called "Cohomology of Algebraic groups" and it explains that generic cohomology of a finite dimensional module equals discrete cohomology because the projective limit satisfies the Mittag-Leffler condition.
Sep
23
comment cohomology theory for algebraic groups
@David_Stuart. Am I missing a projective limit? Is the argument of van der Kallen that this is the kind of limit that is treated by J. E. Roos in LNM 92, Berlin 1969 ?
Sep
23
comment cohomology theory for algebraic groups
Why refer to something that is difficult to get hold of? Just refer to our 1977 Inventiones paper which was a joint paper for good reasons.
Sep
22
revised How to prove this polynomial always has integer values at all integers?
91 replaced with 153
Sep
22
revised How to prove this polynomial always has integer values at all integers?
three inequalities corrected
Sep
21
revised How to prove this polynomial always has integer values at all integers?
one more number corrected
Sep
21
revised How to prove this polynomial always has integer values at all integers?
two numbers changed
Sep
18
awarded  Nice Answer
Sep
18
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Sep
18
awarded  Revival
Sep
18
revised How to prove this polynomial always has integer values at all integers?
deleted 11 characters in body
Sep
18
answered How to prove this polynomial always has integer values at all integers?
Sep
9
comment Questions about $\mathbb{C}[G/U^-]$ and $\mathbb{C}[B]$
One must use the action on $\mathbb C[B]$ from the left and from the right. Filter by requiring that weights are no further than $d$ from zero for both actions. That is, look at maximal submodules (for the double action) with that property. This gives a canonical filtration which one should make explicit in terms of the coordinates. You should find multiplicities for $d$ less than 5.
Sep
7
comment Questions about $\mathbb{C}[G/U^-]$ and $\mathbb{C}[B]$
The P(−λ) are the $V(λ)^*$ of Jianrong Li, so there must be multiplicities. It must already be visible for $SL_2$ that there are multiplicities so that the map $\bigoplus_{h\in S} M_\lambda^* \to \mathbb{C}[B]$ is not surjective.
Sep
7
comment Questions about $\mathbb{C}[G/U^-]$ and $\mathbb{C}[B]$
The paper was about longest weight vectors, not just lowest weight vectors.