Search Results

This question is motivated by this one. Basically, the remark of Bugs Bunny in comments made me think - OK, there is an ambiguity in choosing between a Young diagram and its transpose when constructin …

I think so. The key property used in the proof is $$ Res^G_H Ind^G_H V=\bigoplus_{s\in H\setminus G/H} Ind^H_{H_s}V_s, $$ where $V_s$ is the twist of $V$ by $s$, and $H_s=sHs^{-1}\cap H$, and its p …

For how you can explain the precise relationship between Cherednik algebras and stuff from classical algebraic geometry/commutative algebra, you can, for example, check out papers http://arxiv.org/ab …

I recall your question on a related topic... I am sure that associativity is assumed here (and just omitted because the audience is unlikely to think of any other algebras); as for unitality, won't …

Operads that are quotients of the associative operad (which I believe your updated question is aimed at) are, in characteristic zero, fairly extensively studied since the 1950s or so, under the somewh …

It seems that in some particular cases it is known, see e.g. this recent result. I was looking at that a while ago, and at least it became clear to me that one has to be very careful with lifting the …

Yes. See the result of Section 2.5 of a wonderful paper of Bernhard Keller : https://webusers.imj-prg.fr/~bernhard.keller/publ/ilc.pdf (and the references therein).

Yes your series of representations looks (except for the first term - but there must be the law of small numbers lurking around) like the sign representation times the Whitehouse module, see, e.g. th …

I think this might be so standard that there is no obvious reference. The cohomology has a basis of Schubert classes. In the adjoint case, Schubert classes are indexed by the Weyl group orbit of the h …

I believe that you should consult the book "Double affine Hecke algebras" by Cherednik, more specifically Section 3.7, more specifically Theorem 3.7.2.

Interesting/uninteresting is a very subjective thing, so let me try to just say several things that I see immediately. 0) This algebra, unlike the Witt algebra, does not have any [obvious] grading, …

The method/result you are looking for is commonly known under the name "unitary trick" (of Hurwitz and Weyl), - this keyword should bring you a great deal of accessible explanations of all possible le …

I think your question, the way it is stated, makes one want to classify unary and binary (depending how far you generalise the question as written) invariant differential operators on tensor fields. T …

What kind of a formula will you find satisfactory? Formulas for the plethysm $s_\lambda\circ h_n$ where coefficients are expressed in terms of $S_n$-characters and generalized Kostka numbers are in Ma …

You might want to look at the paper Groebner bases of ideals invariant under endomorphisms by Drensky and La Scala.