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Jucys-Murphy Elements for Brauer Algebra #18798
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Branch pushed to git repo; I updated commit sha1. New commits:
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Commit: |
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
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comment:7
Sorry, this git history is hard to read! The only change this ticket should include over 18762 is the |
comment:8
Is this ready for review? A few things from a quick lookover: Make the reference key |
comment:10
Yeah, this is ready for review. Thank you for the suggestions thus far! |
comment:11
A couple of suggestions: def jucys_murphy(self, j):
r"""
- Return a generalized Jucys-Murphy elements for the Brauer algebra.
- These are outlined in [Naz]_.
+ Return the ``j``-th generalized Jucys-Murphy element of ``self``.
+ Could you give a more detailed description of how the elements are defined?
+
REFERENCES:
.. [Naz] Maxim Nazarov, Young's Orthogonal Form for Brauer's Centralizer
- Algebra. Journal of Algebra 182 (1996), 664--693.
+ Algebra. Journal of Algebra 182 (1996), 664--693.
EXAMPLES:
sage: z = var('z')
sage: B = BrauerAlgebra(3,z)
sage: B.jucys_murphy(1)
1/2*z - 1/2
sage: B.jucys_murphy(3)
- -B{{-3, -2}, {-1, 1}, {2, 3}} - B{{-3, -1}, {-2, 2}, {1, 3}} + B{{-3, 1}, {-2, 2}, {-1, 3}} + B{{-3, 2}, {-2, 3}, {-1, 1}} + (1/2*z-1/2)*B{{-3, 3}, {-2, 2}, {-1, 1}}
+ -B{{-3, -2}, {-1, 1}, {2, 3}} - B{{-3, -1}, {-2, 2}, {1, 3}}
+ + B{{-3, 1}, {-2, 2}, {-1, 3}} + B{{-3, 2}, {-2, 3}, {-1, 1}}
+ + (1/2*z-1/2)*B{{-3, 3}, {-2, 2}, {-1, 1}}
"""
- B = self
- return (B._q-1)/2 + sum(B([[i,-j],[j,-i]]) - B([[i,j],[-i,-j]]) for i in range(1,j))
+ I = self._indices
+ one = self.base_ring().one()
+ return ((self._q-1)/2
+ + self._from_dict({I([[i,-j],[j,-i]]): one for i in range(1,j)}, remove_zeros=False)
+ - self._from_dict({I([[i,j],[-i,-j]]): one for i in range(1,j)}, remove_zeros=False)) Do you think we should also make this a cached method? What about when |
Branch pushed to git repo; I updated commit sha1. New commits:
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comment:13
Alright, I added a small explanation to the docstring, and also took into account the one element of base ring. However, the problem with your |
Changed branch from u/ghseeli/jucys_murphy_elements_for_brauer_algebra to u/tscrim/jucys_murphy_elements-18798 |
Reviewer: Travis Scrimshaw |
comment:14
I made some minor tweaks to the documentation. The reason why I use the New commits:
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comment:15
Alright. I am satisfied with these changes. Good catch on the first element! |
Changed branch from u/tscrim/jucys_murphy_elements-18798 to |
Nazarov's 1996 paper titled "Young's Orthogonal Form for Brauer's Centralizer Algebra," outlines a form for the Jucys-Murphy elements that are analogous to the JM elements for the symmetric group algebra. Implementing these into Sage would require a few lines of code but would prove very useful for work done with the Brauer algebra.
Depends on #18762
CC: @alauve @srdoty @saliola @tscrim
Component: algebra
Keywords: days65, partition algebra, diagram algebra, jucys-murphy
Author: George H. Seelinger
Branch/Commit:
9613ee3
Reviewer: Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/18798
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