T. Jozefiak, P. Pragacz and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109--189.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have been studied by several authors and are known to possess a number of nice properties. For example, Pfaan rings are CohenMacaulay normal domains, which are, in fact, factorial and Gorenstein (cf. 3,30,37] Height, depth and in some cases, the minimal resolution of Pfaan ideals is known (cf. [28,29,38]) The singular locus of Pfaan rings is known Partially supported by a Career Award grant from AICTE, New Delhi and an IRCC grant from IIT Bombay. Partially supported by the Austrian Science Foundation FWF, grant P13190MAT. Current Address: Institut Girard Desargues, Universit e Claude ....

T. Joze ak, P. Pragacz and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and skew-symmetric matrices, in: Young tableaux and Schur Functors in Algebra and Geometry (Torun,

....k) which is crucial for Lascoux s 1991 Mathematics Subject Classification. 14M12, 18G10, 13C14, 14M25, 05E15, 05E25, Typeset by A M S T E X analysis, and his result actually describes the decomposition of Tor ffl (M; k) into GLm (k) Theta GL n (k) irreducibles. J ozefiak, Pragacz, and Weyman [JPW] used similar methods to compute Tor ffl (M; k) where A is the polynomial ring k[z ij ] in the entries of a generic n Theta n symmetric matrix (z ij = z ji ) I is the ideal generated by all t Theta t minors, and M is the quotient A=I (again k has characteristic zero) Their results also rely ....

.... t minors, and M is the quotient A=I (again k has characteristic zero) Their results also rely heavily on the inherent GL n (k) action, and describe the irreducible GL n (k) decomposition of Tor ffl (M; k) The main results of this paper will generalize the results for 2 Theta 2 minors from [La, JPW], as we now explain. Let k[x; y] k[x 1 ; xm ; y 1 ; y n ] be a polynomial ring in two sets of variables of sizes m;n respectively. The Segre subalgebra Segre(m; n; 0) is the subalgebra generated by all monomials x i y j with 1 i m and 1 j n. Letting A m;n be the polynomial ....

[Article contains additional citation context not shown here]

T. J'ozefiak, P. Pragacz, and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109-189.

....14M25, 05E15, 05E25. Typeset by A M S T E X is an action of GLm (k) Theta GL n (k) on Tor ffl (M; k) which is crucial for Lascoux s analysis, and his result actually describes the decomposition of Tor ffl (M; k) into GLm (k) Theta GL n (k) irreducibles. J ozefiak, Pragacz, and Weyman [JPW] used similar methods to compute Tor ffl (M; k) where A is the polynomial ring k[z ij ] in the entries of a generic n Theta n symmetric matrix (z ij = z ji ) I is the ideal generated by all t Theta t minors, and M is the quotient A=I (again k has characteristic zero) Their results also rely ....

.... t minors, and M is the quotient A=I (again k has characteristic zero) Their results also rely heavily on the inherent GL n (k) action, and describe the irreducible GL n (k) decomposition of Tor ffl (M; k) The main results of this paper will generalize the results for 2 Theta 2 minors from [La, JPW], as we now explain. Let k[x; y] k[x 1 ; xm ; y 1 ; y n ] be a polynomial ring in two sets of variables of sizes m;n respectively. The Segre subalgebra Segre(m; n; 0) is the subalgebra generated by all monomials x i y j with 1 i m and 1 j n. Letting A m;n be the polynomial ....

[Article contains additional citation context not shown here]

T. J'ozefiak, P. Pragacz, and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109-189.

....The expected dimension of the degeneracy locus D k (OE) is ae = n Gamma in the symmetric case, and ae = n Gamma in the skew symmetric case. When this dimension is correct, the minimal resolution K Gamma I Gamma 0 of the ideal sheaf of D k (OE) has been computed in [8] : if OE is symmetric, i=jj l(l Gamma1) 2 S (k Gamma1) E where l has to be even, while if OE is skew symmetric and k is even, i=jj l(l 1) 2 S (k 1) E With the very same proof, Theorem E extends in the following way : Theorem F. Let OE : E L be a symmetric or skew symmetric ....

J'ozefiak T., Pragacz P., Weyman J. : Resolution of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, in Tableaux de Young et foncteurs de Schur en algbre et gomtrie, Astrisque 87-88, 109-189 (1981).

....13C14 , 13H10 . Typeset by A M S T E X of GLm (k) Theta GL n (k) on A; I; M and Tor ffl (M; k) which is crucial for Lascoux s analysis, and his result actually describes the decomposition of Tor ffl (M; k) into GLm (k) Theta GL n (k) irreducibles. Later, J ozefiak, Pragacz, and Weyman [JPW] used similar methods to compute Tor ffl (M; k) where A is the polynomial ring k[z ij ] in the entries of a generic n Theta n symmetric matrix (z ij = z ji ) and the module M is the quotient A=I, with I generated by all t Theta t minors (again k has characteristic zero) Their results also ....

.... I generated by all t Theta t minors (again k has characteristic zero) Their results also rely heavily on the inherent GL n (k) action, and describe the irreducible GL n (k) decomposition of Tor ffl (M; k) The main results of this paper will generalize the results for 2 Theta 2 minors from [La, JPW], as we now explain. Let k[x; y] k[x 1 ; xm ; y 1 ; y n ] be a polynomial ring in two sets of variables of sizes m;n respectively. The Segre subalgebra Segre(m; n; 0) is the subalgebra generated by all monomials x i y j with 1 i m and 1 j n, Letting A m;n be the polynomial ....

[Article contains additional citation context not shown here]

T. J'ozefiak, P. Pragacz, and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109-189.

....U(V ) Delta Delta Delta U p (V ) U p Gamma1 (V ) This complex arose in J ozefiak Weyman [9] as the Koszul complex over Sym V of the ideal generated by Sym 2 V in Sym V . We refer to it as the JW complex. The following theorem is stated in [9] and implicitly proved in [8]. Theorem 2.5 (J ozefiak Weyman [9] For all p 2 N, the following isomorphism of GL(V ) modules holds H p (U(V ) GL(V ) M : 0 d( jj Gamma 2p V : 2.1) The Reiner Roberts Theorem (Theorem 2.2) and the J ozefiak Weyman Theorem (Theorem 2.5) together imply that the homology ....

T. J'ozefiak, P. Pragacz and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Ast'erisque 87-88 (1981), 109-189.

....free resolution, matching complex, chessboard complex, determinantal ideals. Typeset by A M S T E X 1 2 VICTOR REINER AND JOEL ROBERTS analysis, and his result actually describes the decomposition of Tor A ffl (M; k) into GLm (k) Theta GL n (k) irreducibles. J ozefiak, Pragacz, and Weyman [JPW] used similar methods to compute Tor A ffl (M; k) where A is the polynomial ring k[z ij ] in the entries of a generic n Theta n symmetric matrix (z ij = z ji ) I is the ideal generated by all t Theta t minors, and M is the quotient A=I (again k has characteristic zero) Their results also ....

.... t minors, and M is the quotient A=I (again k has characteristic zero) Their results also rely heavily on the inherent GL n (k) action, and describe the irreducible GL n (k) decomposition of Tor A ffl (M; k) The main results of this paper will generalize the results for 2 Theta 2 minors from [La, JPW], as we now explain. Let k[x; y] k[x 1 ; xm ; y 1 ; y n ] be a polynomial ring in two sets of variables of sizes m;n respectively. The Segre subalgebra Segre(m; n; 0) is the subalgebra generated by all monomials x i y j with 1 i m and 1 j n. Letting A m;n be the polynomial ....

[Article contains additional citation context not shown here]

T. J'ozefiak, P. Pragacz, and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109-189.

....locus D k (OE) is ae = n Gamma Gamma e Gammak 1 2 Delta in the symmetric case, and ae = n Gamma Gamma e Gammak 2 Delta in the skew symmetric case. When this dimension is correct, the minimal resolution K ffl Gamma I Gamma 0 of the ideal sheaf of D k (OE) has been computed in [7]: if OE is symmetric, K i = M = l; i=j j l(l Gamma1) 2 S (k Gamma1) E ; where l has to be even, while if OE is skew symmetric and k is even, K i = M = l; i=j j l(l 1) 2 S (k 1) E : With the very same proof, Theorem E extends in the following way: Theorem H. ....

J'ozefiak T., Pragacz P., Weyman J.: Resolution of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, in Tableaux de Young et foncteurs de Schur en algbre et gomtrie, Astrisque 87-88, 109-189 (1981).

No context found.

T. Jozefiak, P. Pragacz and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices, Asterisque 87-88 (1981), 109--189.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC