32,797 reputation
370144
bio website math.umass.edu/~jeh
location U. Massachusetts, Amherst
age 75
visits member for 5 years, 5 months
seen 6 hours ago
More-or-less retired professor at UMass Amherst. Basically an algebraist with interests in Lie theory, specifically representation theory and related algebraic geometry.

1d
comment How to associate a proper parabolic subgroup of a real s.s Lie group $G$ to a non-trivial unipotent element in a non uniform lattice in $G$?
Since the 1972 Borel-Tits paper is referred to here and in the link just posted by grghxy, maybe it's a good idea to add a link to it (though it's in French): gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002088894
1d
comment How to associate a proper parabolic subgroup of a real s.s Lie group $G$ to a non-trivial unipotent element in a non uniform lattice in $G$?
This is a useful approach, but it's a good idea to add an explicit reference/link to the Borel-Tits result. (The question asked could also use more background.) Note too that the "unipotent" concept here requires identification of the complex Lie group with an algebraic group where the Jordan decomposition makes sense. Then the real group is the group of real points, etc.
1d
revised How to associate a proper parabolic subgroup of a real s.s Lie group $G$ to a non-trivial unipotent element in a non uniform lattice in $G$?
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2d
comment Does anyone have an electronic copy of Waldspurger's “Sur les coefficients de Fourier des formes modulaires de poids demi-entier”?
@David: It might have helped matters to include the page numbering, since the article is over 100 pages long (and has been very often cited, indicating its influence). So far Elsevier's Science Direct have not reached back nearly so far in their archive to create searchable PDF files, though they now permit free access to older papers which have PDF versions.
Jul
27
revised 1-dimensional representations of the affine Hecke algebra for $SL_2$
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Jul
26
comment Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
@hic: Concerning your question, the answer is certainly yes (see Carter's extensive discussion in his Chapter 5, in particular Prop. 5.7.3 where $P$ denotes the JM parabolic. Your example is a good one to illustrate what is going on.
Jul
26
answered 1-dimensional representations of the affine Hecke algebra for $SL_2$
Jul
25
comment Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
P.S. I've tried to make my answer more precise, but the details here are rather complicated to spell out.
Jul
25
revised Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
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Jul
25
comment Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
@hic: Concerning Richardson orbits, it's a good idea to look at a textbook like the one by Collingwood-McGovern (or Carter's 1985 book). Basically, to each parabolic subalgebra corresponds a nilpotent orbit determined by the dense orbit in its nilradical, and in type $A_n$ all nilpotent orbits occur this way (but not in general). Concerning $SL_3$, I'll double-check the details; but what you say doesn't sound correct.
Jul
25
revised Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
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Jul
25
answered Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
Jul
25
revised Characterizations of Jacobson-Morozov parabolics associated to a nilpotent
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Jul
25
comment 1-dimensional representations of the affine Hecke algebra for $SL_2$
It's essential to distinguish carefully between the "affine Weyl group" (or Hecke algebra) and the "extended" version, both of which enter into the work of Kazhdan-Lusztig and others influenced by them. (In this direction, it would also be very helpful to indicate which sources you are primarily relying on.)
Jul
24
revised What are the “tensor-closed” object of the BGG category $\mathcal{O}$ of a semisimple Lie algebra $\mathfrak{g}$?
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Jul
24
answered Invariants of the maximal unipotent subgroup of GL(n) acting on the space of n by n matrices
Jul
24
revised highest weight the half-sum of positive roots
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Jul
23
revised highest weight the half-sum of positive roots
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Jul
23
answered highest weight the half-sum of positive roots
Jul
22
answered Linear Algebra classic books