19,507 research outputs found
Unipotent elements forcing irreducibility in linear algebraic groups
Let be a simple algebraic group over an algebraically closed field of
characteristic . We consider connected reductive subgroups of
that contain a given distinguished unipotent element of . A result of
Testerman and Zalesski (Proc. Amer. Math. Soc., 2013) shows that if is a
regular unipotent element, then cannot be contained in a proper parabolic
subgroup of . We generalize their result and show that if has order ,
then except for two known examples which occur in the case ,
the subgroup cannot be contained in a proper parabolic subgroup of . In
the case where has order , we also present further examples arising
from indecomposable tilting modules with quasi-minuscule highest weight.Comment: 33 page
Well-fuctioning home composters
In recent years, the Work Efficiency Institute (TTS) has compared thermal composters, regulating materials and compost accelerators and studied user's experiences on home composting by a questionnaire. The aim has been to produce information on composting, so that home composting can be made as easy as possible
Magnetic fields of cool giant and supergiant stars: models versus observations
The recent years have brought great advances in our knowledge of magnetic
fields in cool giant and supergiant stars. For example, starspots have been
directly imaged on the surface of an active giant star using optical
interferometry, and magnetic fields have been detected in numerous slowly
rotating giants and even on supergiants. Here, I review what is currently known
of the magnetism in cool giant and supergiant stars, and discuss the origin of
these fields and what is theoretically known about them.Comment: 7 pages, 2 figures, invited review in the conference "Stars with a
stable magnetic field: from pre-main sequence to compact remnants", to be
published in Contributions of the Astronomical Observatory Skalnate Ples
Invariant forms on irreducible modules of simple algebraic groups
Let be a simple linear algebraic group over an algebraically closed field
of characteristic and let be an irreducible rational
-module with highest weight . When is self-dual, a basic
question to ask is whether has a non-degenerate -invariant alternating
bilinear form or a non-degenerate -invariant quadratic form.
If , the answer is well known and easily described in terms of
. In the case where , we know that if is self-dual, it
always has a non-degenerate -invariant alternating bilinear form. However,
determining when has a non-degenerate -invariant quadratic form is a
classical problem that still remains open. We solve the problem in the case
where is of classical type and is a fundamental highest weight
, and in the case where is of type and for . We also give a solution in some specific
cases when is of exceptional type.
As an application of our results, we refine Seitz's description of
maximal subgroups of simple algebraic groups of classical type. One consequence
of this is the following result. If are simple
algebraic groups and is irreducible, then one of the following
holds: (1) is not self-dual; (2) both or neither of the
modules and have a non-degenerate invariant
quadratic form; (3) , , and .Comment: 46 pages; to appear in J. Algebr
The first close-up of the "flip-flop" phenomenon in a single star
We present temperature maps of the active late-type giant FK Com which
exhibit the first imagining record of the ``flip-flop'' phenomenon in a single
star. The phenomenon, in which the main part of the spot activity shifts 180
degrees in longitude, discovered a decade ago in FK Com, was reported later
also in a number of RS CVn binaries and a single young dwarf. With the surface
images obtained right before and after the ``flip-flop'', we clearly show that
the ``flip-flop'' phenomenon in FK Com is caused by changing the relative
strengths of the spot groups at the two active longitudes, with no actual spot
movements across the stellar surface, i.e. exactly as it happens in other
active stars.Comment: 4 pages, accepted by A&A Letter
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