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Results tagged with rt.representation-theory
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user 10881
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
7
votes
Symmetric powers of Schur polynomials
this could be done in sage:
sage: B3 = WeylCharacterRing("B3", style="coroots")
sage: spin = B3(0,0,1)
sage: spin.symmetric_power(6)
B3(0,0,0) + B3(0,0,2) + B3(0,0,4) + B3(0,0,6)
sage: A3 = WeylChar …
- 3,597
7
votes
Accepted
Super-plethysm?
This amounts to study composition of "linear species" in the category of complexes.
The correct way to handle these computations using plethysm is
to introduce an auxiliary variable $t$ and to weight …
- 3,597
4
votes
Temperley-Lieb algebras for other Weyl groups?
There are some ad-hoc definitions for some types. Type B can be defined using diagrams that have a left-right symmetry. Tammo tom Dieck has proposed a definition for type D here: (http://www.uni-math. …
- 3,597
3
votes
Breaking up the free Lie algebra into GL irreps
Here is the result, computed using sage:
sage: def lie(n):
....: p = SymmetricFunctions(QQ).p()
....: return p.sum_of_terms((Partition([d for j in range(ZZ(n / d))]),
....: …
- 3,597
3
votes
Compute formal character of semisimple Lie algebras.
You can use sage for this (and for many other things)
See the following manual page:
The Weyl character ring
- 3,597
2
votes
Accepted
Number of cluster variables
For $A_k$ of level $\ell$, the cluster types are given by square grids of size $k \times \ell$.
Therefore the types you ask for are $E_6$ and $E_8$ (see Scott - Grassmannians and cluster algebras), fo …
- 3,597
2
votes
Matrix of cosecants appearing in equivariant index computations
Some sage code for experimental purposes:
def matr(p):
N = (p - 1) / 2
return matrix(N, N, lambda i,j: sin(pi/p*(i+1)*(j+1))**-2)
Resulting in
sage: [(p,matr(p).change_ring(QQbar).det()) …
- 3,597
2
votes
Accepted
Rigid, maximal rigid and cluster-tilting objects
For rigid and maximal rigid, you can think instead in the category of quiver representations.
The term "rigid" comes from the fact that the vanishing of Ext^1 can be understood as the absence of any t …
- 3,597
1
vote
About cluster variables obtained by (sequentially) mutating at exchangeable variables from a...
Not really an answer, but a comment about the related question:
Can one reach every cluster in that way ?
It is rather easy to check (using sagemath or Keller's applet) that for the cyclic quiver in …
- 3,597