caa a22 4500 606161082 CHVBK 20210128100633.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10468-015-9541-z doi (NATIONALLICENCE)springer-10.1007/s10468-015-9541-z Dolce Salvatore Dipartimento di Matematica, Università La Sapienza di Roma, P.le Aldo Moro 5, 00185, Rome, Italy aut On Certain Modules of Covariants in Exterior Algebras [Elektronische Daten] [Salvatore Dolce] We study the structure of the space of covariants B : = ∧ ( 𝔤 / 𝔨 ) ∗ ⊗ 𝔤 𝔨 , $B:=\left (\bigwedge (\mathfrak {g}/\mathfrak {k})^{*}\otimes \mathfrak {g}\right )^{\mathfrak {k}},$ for a certain class of infinitesimal symmetric spaces ( 𝔤 , 𝔨 ) $(\mathfrak {g},\mathfrak {k})$ such that the space of invariants A : = ∧ ( 𝔤 / 𝔨 ) ∗ 𝔨 $A:=\left (\bigwedge (\mathfrak {g}/\mathfrak {k})^{*}\right )^{\mathfrak {k}}$ is an exterior algebra ∧(x 1,...,x r ), with r = rk ( 𝔤 ) − rk ( 𝔨 ) $r=rk(\mathfrak {g})-rk(\mathfrak {k})$ .We prove that they are free modules over the subalgebra A r−1=∧(x 1,...,x r−1) of rank 4r. In addition we will give an explicit basis of B. As particular cases we will recover same classical results. In fact we will describe the structure of ∧ ( M n ± ) ∗ ⊗ M n G $\left (\bigwedge (M_{n}^{\pm })^{*}\otimes M_{n}\right )^{G}$ , the space of the G−equivariant matrix valued alternating multilinear maps on the space of (skew-symmetric or symmetric with respect to a specific involution) matrices, where G is the symplectic group or the odd orthogonal group. Furthermore we prove new polynomial trace identities. Springer Science+Business Media Dordrecht, 2015 Invariant theory nationallicence Symmetric spaces nationallicence Exterior algebras nationallicence Polynomial trace identities nationallicence Algebras and Representation Theory Springer Netherlands 18/5(2015-10-01), 1299-1319 1386-923X 18:5<1299 2015 18 10468 https://doi.org/10.1007/s10468-015-9541-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9541-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dolce Salvatore Dipartimento di Matematica, Università La Sapienza di Roma, P.le Aldo Moro 5, 00185, Rome, Italy aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/5(2015-10-01), 1299-1319 1386-923X 18:5<1299 2015 18 10468