Spinor structures on free resolutions of codimension four Gorenstein ideals

We analyze the structure of spinor coordinates on resolutions of Gorenstein ideals of codimension four. As an application we produce a family of such ideals with seven generators which are not specializations of Kustin-Miller model.
Comment: 26 pages, 1 figure, 2 tables Major changes: 1) Section 2: Background in Representation Theory (new section). 2) Revised section 3 (The background on free resolutions). 3) Revised Definition 4.1, modified the statement of Theorem 4.2, added a new Remark 4.3, and revised the proof of Theorem 4.2. 4) Examples in sections 5, 6, and 7 are also revised