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Math Grad Student


Apr
21
revised Automorphism group of Fano Plane
added some more details.
Apr
21
answered Automorphism group of Fano Plane
Apr
21
comment The 9 Billion Names of God
Is there a nice expression for the partial sums of $\sum G_nx^n$?
Apr
21
comment Casimir element of a universal enveloping algebra
over the next couple pages it related these two Casimir elements.
Apr
21
comment Casimir element of a universal enveloping algebra
look carefully! That is for $U_q(sl_2)$ which is actually a deformation of $U(sl_2)$. These are different algebras.
Apr
20
answered Casimir element of a universal enveloping algebra
Apr
18
answered Problems that differential geometry solves
Apr
14
answered Inverse Image as the left adjoint to pushforward
Apr
10
comment Meaning of pullback
Have a look at this question of mine: math.stackexchange.com/questions/10180/…
Apr
6
comment Good resources (book or otherwise) to learn/study basic Combinatorics
@Fixee there have been many many editions.
Mar
28
comment Question about notation / terminology
you should consider a different title that gives an idea of what this question is about.
Mar
16
comment Geometric mean never exceeds arithmetic mean
Not what you are looking for, but the Lagrange multipliers proof is pretty slick. Just take the geometric mean as the function to minimize and the constraint $\sum_{i=1}^n x_i=n$.
Mar
16
comment How to compute the Gel'fand Models for a (quantum) Lie Algebra
@Mariano again thanks for the reference. I have looked through the connections to this paper on google and on MathSciNet to no avail. But I do know some things. In the case of the classical case, using what we know about homogeneous coordinate rings, we can get a decent presentation of the rings by taking the embedding into the product of $Gr(i,n)$ by Plucker relations. An explicit description is found in Miller-Sturmfeld Combinatorial commutative algebra chapter 14. For the quantum case I have no idea. Literally the only thing I can find is the $sl_2$ case,I would be very happy to see others.
Mar
15
comment Why is the coordinate ring of a projective variety not determined by the isomorphism class of the variety?
consider scaling the grading for a graded ring, and taking the proj construction. Details can be found in 7.4 of Ravi Vakil's notes: math.stanford.edu/~vakil/216blog/FOAGmar1011public.pdf
Mar
15
comment How to compute the Gel'fand Models for a (quantum) Lie Algebra
@Mariano, Thanks for the reference, I will take a look. In the mean time, I have edited the question to reflect this enlightenment. Thanks again.
Mar
15
revised How to compute the Gel'fand Models for a (quantum) Lie Algebra
made the question suck less
Mar
15
comment How to compute the Gel'fand Models for a (quantum) Lie Algebra
@Mariano Well damn. I am really looking for the Homogeneous coordinate ring for the flag variety. This coincides with the definition I have just mentioned. Now that I look through my references, I am having difficulty finding it referred to as such. However here is at least one case: arxiv.org/PS_cache/math/pdf/0010/0010042v4.pdf (in the first paragraph). I am sorry for the confusion. Thank you for your patience, I will edit the question.
Mar
15
comment How to compute the Gel'fand Models for a (quantum) Lie Algebra
Consider the action of $sl_2$ on the standard basis of $C<x,y>$ by the liebniz action. This makes a highest weight repesentation with weight given by power of $x$. The action moves the power to $y$. Thus, taking the ring generated by these weight spaces is $C[x,y]$. In this sense, $R(sl_2)=\oplus_{\lambda\in P^+}V(\lambda)$ for $P^+$ the dominant weights and $V(\lambda)$ the corresponding weight representation. This is what I mean. I hope is is clear. Also, I am typing on the iPad, sorry if the Tex sucks.
Mar
14
accepted Stacks are just sheaves up to Isomorphism
Mar
14
accepted Is restriction of scalars a pullback?