On Minuscule Representations and the Principal SL
Thus, the W-orbits of minuscule coweights correspond bijectively to simple roots α with multiplicity 1 in the highest root β If λ is minuscule and dominant, g λ (1) is the
Combinatorics of minuscule representations
It is useful to reinterpret the transitive W-action on Wλas the action on cosets W/WS−s, where WS−s is the maximal parabolic subgroup of W fixing λ; a minuscule highest weight λ is always one of the fundamental weights, fixed by all but one simple reflection s among the Coxeter generators S for W Stembridge[8] showed that the set WS
ON DOMINANCE AND MINUSCULE WEYL GROUP ELEMENTS
ON DOMINANCE AND MINUSCULE WEYL GROUP ELEMENTS QENDRIM R GASHI AND TRAVIS SCHEDLER¨ ABSTRACT Fix a Dynkin graph and let ‚ be a coweight When does there exist an element w of the corre-sponding Weyl group such that w is ‚-minuscule and w(‚) is dominant? We answer this question for general Coxeter groups
Homomesy in Minuscule Posets - MIT Mathematics
root We can now de ne a minuscule representation De nition 7 A representation is considered minuscule if every weight is of the form w , where w2W, the corresponding Weyl Group of the representation, and is the maximal weight with respect to the root order This type of representation is equivalent to saying that the Weyl group acts transitively
On the Minuscule Representation of Types and
these representations, minuscule representations play an important role It is known that the minuscule representations of simple Lie algebras are irre-ducible My goal is to show the irreducibility of a minuscule representation using only the cycle structures of the Weyl group elements viewed as permutations acting
Small resolutions of minuscule Schubert varieties
minuscule Schubert varities by B D Boe in [Bo] and we hope that our construction will lead to a geometric interpretation of these results In order to define our resolutions, we introduce a combinatorial objet: a quiver associated to a minuscule Schubert variety X(w) This quiver is defined thanks to a reduced writing weof
Small resolutions of minuscule Schubert varieties
natorial way for all minuscule Schubert varieties by Boe [Boe88] and we hope that our construction will lead to a geometric interpretation of these results Schubert varieties X(w) are parametrized by elements w of a Weyl group W In order to define our resolutions, we introduce a combinatorial object: to any reduced expression w of the element w,
ON MINUSCULE REPRESENTATIONS AND THE PRINCIPAL SL
The element is a dominant, minuscule co-weight if and only if there is a single simple root with h ; i=1, the root has multiplicity 1 in the highest root , and all other simple roots 0satisfy h ; i=0 Thus, the W-orbits of minuscule co-weights correspondbijectively to simple roots with multiplicity 1 in the highest root If is minuscule and
List of New Testament minuscules - holybibleinstitutecom
Codex Ebnerianus, Minuscule 105, (12th), John 1:5b-10 A New Testament minuscule is a copy of a portion of the New Testament written in a small, cursive Greek script (developed from Uncial) [1][2] Most of the minuscules are still written on parchment Paper was used since the 12th century New Testament minuscules are distinct from:
Teachers’ Resource: Minuscule – Valley Of The Lost Ants
Minuscule – Valley Of The Lost Ants Dirs: Thomas Szabo, Hélène Giraud France/Belgium 2016 / 1h29m Synopsis Minuscule is a charming film which combines animation with live footage shot in the Mercantour and Les Ecrins National Parks in Southern France As well as being an epic
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