By Roger W. Carter, Meinolf Geck
The illustration concept of reductive algebraic teams and comparable finite reductive teams has many functions. The articles during this quantity supply introductions to numerous points of the topic, together with algebraic teams and Lie algebras, mirrored image teams, abelian and derived different types, the Deligne-Lusztig illustration thought of finite reductive teams, Harish-Chandra thought and its generalizations, quantum teams, subgroup constitution of algebraic teams, intersection cohomology, and Lusztig's conjectured personality formulation for irreducible representations in leading attribute. The articles are rigorously designed to augment each other, and are written by means of a workforce of exceptional authors: M. Brou?, R. W. Carter, S. Donkin, M. Geck, J. C. Jantzen, B. Keller, M. W. Liebeck, G. Malle, J. C. Rickard and R. Rouquier. This quantity as a complete should still offer a truly available creation to an incredible, although technical, topic.
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Additional resources for Representations of reductive groups
C. A head cannot take another head as a complement (Kayne (199): 8). d. A head cannot have more than one complement (Kayne (199): 136, fn. 28). Along with these standard properties of X-bar theories, the following special properties can also be derived from the LCA (via the de®nition of c-command based on the segment/category distinction): (21) a. A speci®er is an adjunct (Kayne (199): 17). b. There can at most be one adjunct/speci®er per phrase (Kayne (199): 22). c. At most one head can adjoin to another head (Kayne (199): 20¨ ).
Let us start with the small clause type, (1a). This structure includes two nonterminals (YP and ZP) that c-command each other and that contain at least another nonterminal (Y 0 and its complement QP, Z 0 and its complement RP); the nonterminals projecting YP and ZP, then, would prevent the tree from linearizing. For the sake of clarity, I represent the situation in greater detail in (11) by indicating the terminals dominated by the head of YP (y) and by the head of ZP (z). , z precedes y). , y precedes z).
The situation parallels the one in (14); that is, (F, L) is a point of symmetry. 8 Limiting ourselves to looking at the LCA-compatible structures, we can see that most stipulated properties of X-bar theoriesÐin particular, the ones listed in (20)Ðcan be derived from the LCA. In what follows I will rely heavily on the schema given in Cinque 1996, 449¨. (from which (20) and (21) are quoted). (20) a. There can be no phrase dominating two (or more) phrases (Kayne (199): 11). b. There cannot be more than one head per phrase (Kayne (199): 8).